Lagrange basis polynomials for equally spaced nodes
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Numbers
$d$
$i$ 
0
0:
1
1
0:
-x + 1
1
1:
x
2
0:
1/2*x^2 - 3/2*x + 1
2
1:
-x^2 + 2*x
2
2:
1/2*x^2 - 1/2*x
3
0:
-1/6*x^3 + x^2 - 11/6*x + 1
3
1:
1/2*x^3 - 5/2*x^2 + 3*x
3
2:
-1/2*x^3 + 2*x^2 - 3/2*x
3
3:
1/6*x^3 - 1/2*x^2 + 1/3*x
4
0:
1/24*x^4 - 5/12*x^3 + 35/24*x^2 - 25/12*x + 1
4
1:
-1/6*x^4 + 3/2*x^3 - 13/3*x^2 + 4*x
4
2:
1/4*x^4 - 2*x^3 + 19/4*x^2 - 3*x
4
3:
-1/6*x^4 + 7/6*x^3 - 7/3*x^2 + 4/3*x
4
4:
1/24*x^4 - 1/4*x^3 + 11/24*x^2 - 1/4*x
5
0:
-1/120*x^5 + 1/8*x^4 - 17/24*x^3 + 15/8*x^2 - 137/60*x + 1
5
1:
1/24*x^5 - 7/12*x^4 + 71/24*x^3 - 77/12*x^2 + 5*x
5
2:
-1/12*x^5 + 13/12*x^4 - 59/12*x^3 + 107/12*x^2 - 5*x
5
3:
1/12*x^5 - x^4 + 49/12*x^3 - 13/2*x^2 + 10/3*x
5
4:
-1/24*x^5 + 11/24*x^4 - 41/24*x^3 + 61/24*x^2 - 5/4*x
5
5:
1/120*x^5 - 1/12*x^4 + 7/24*x^3 - 5/12*x^2 + 1/5*x
6
0:
1/720*x^6 - 7/240*x^5 + 35/144*x^4 - 49/48*x^3 + 203/90*x^2 - 49/20*x + 1
6
1:
-1/120*x^6 + 1/6*x^5 - 31/24*x^4 + 29/6*x^3 - 87/10*x^2 + 6*x
6
2:
1/48*x^6 - 19/48*x^5 + 137/48*x^4 - 461/48*x^3 + 117/8*x^2 - 15/2*x
6
3:
-1/36*x^6 + 1/2*x^5 - 121/36*x^4 + 31/3*x^3 - 127/9*x^2 + 20/3*x
6
4:
1/48*x^6 - 17/48*x^5 + 107/48*x^4 - 307/48*x^3 + 33/4*x^2 - 15/4*x
6
5:
-1/120*x^6 + 2/15*x^5 - 19/24*x^4 + 13/6*x^3 - 27/10*x^2 + 6/5*x
6
6:
1/720*x^6 - 1/48*x^5 + 17/144*x^4 - 5/16*x^3 + 137/360*x^2 - 1/6*x
7
0:
-1/5040*x^7 + 1/180*x^6 - 23/360*x^5 + 7/18*x^4 - 967/720*x^3 + 469/180*x^2 - 363/140*x + 1
7
1:
1/720*x^7 - 3/80*x^6 + 59/144*x^5 - 37/16*x^4 + 319/45*x^3 - 223/20*x^2 + 7*x
7
2:
-1/240*x^7 + 13/120*x^6 - 9/8*x^5 + 71/12*x^4 - 3929/240*x^3 + 879/40*x^2 - 21/2*x
7
3:
1/144*x^7 - 25/144*x^6 + 247/144*x^5 - 1219/144*x^4 + 389/18*x^3 - 949/36*x^2 + 35/3*x
7
4:
-1/144*x^7 + 1/6*x^6 - 113/72*x^5 + 22/3*x^4 - 2545/144*x^3 + 41/2*x^2 - 35/4*x
7
5:
1/240*x^7 - 23/240*x^6 + 69/80*x^5 - 185/48*x^4 + 134/15*x^3 - 201/20*x^2 + 21/5*x
7
6:
-1/720*x^7 + 11/360*x^6 - 19/72*x^5 + 41/36*x^4 - 1849/720*x^3 + 1019/360*x^2 - 7/6*x
7
7:
1/5040*x^7 - 1/240*x^6 + 5/144*x^5 - 7/48*x^4 + 29/90*x^3 - 7/20*x^2 + 1/7*x
8
0:
1/40320*x^8 - 1/1120*x^7 + 13/960*x^6 - 9/80*x^5 + 1069/1920*x^4 - 267/160*x^3 + 29531/10080*x^2 - 761/280*x + 1
8
1:
-1/5040*x^8 + 1/144*x^7 - 73/720*x^6 + 115/144*x^5 - 329/90*x^4 + 349/36*x^3 - 481/35*x^2 + 8*x
8
2:
1/1440*x^8 - 17/720*x^7 + 239/720*x^6 - 179/72*x^5 + 15289/1440*x^4 - 18353/720*x^3 + 621/20*x^2 - 14*x
8
3:
-1/720*x^8 + 11/240*x^7 - 149/240*x^6 + 71/16*x^5 - 268/15*x^4 + 797/20*x^3 - 2003/45*x^2 + 56/3*x
8
4:
1/576*x^8 - 1/18*x^7 + 209/288*x^6 - 179/36*x^5 + 10993/576*x^4 - 1457/36*x^3 + 691/16*x^2 - 35/2*x
8
5:
-1/720*x^8 + 31/720*x^7 - 391/720*x^6 + 2581/720*x^5 - 1193/90*x^4 + 4891/180*x^3 - 141/5*x^2 + 56/5*x
8
6:
1/1440*x^8 - 1/48*x^7 + 61/240*x^6 - 13/8*x^5 + 2803/480*x^4 - 187/16*x^3 + 2143/180*x^2 - 14/3*x
8
7:
-1/5040*x^8 + 29/5040*x^7 - 49/720*x^6 + 61/144*x^5 - 67/45*x^4 + 527/180*x^3 - 103/35*x^2 + 8/7*x
8
8:
1/40320*x^8 - 1/1440*x^7 + 23/2880*x^6 - 7/144*x^5 + 967/5760*x^4 - 469/1440*x^3 + 363/1120*x^2 - 1/8*x
9
0:
-1/362880*x^9 + 1/8064*x^8 - 29/12096*x^7 + 5/192*x^6 - 3013/17280*x^5 + 95/128*x^4 - 4523/2268*x^3 + 6515/2016*x^2 - 7129/2520*x + 1
9
1:
1/40320*x^9 - 11/10080*x^8 + 59/2880*x^7 - 77/360*x^6 + 7807/5760*x^5 - 7667/1440*x^4 + 14139/1120*x^3 - 4609/280*x^2 + 9*x
9
2:
-1/10080*x^9 + 43/10080*x^8 - 7/90*x^7 + 563/720*x^6 - 6787/1440*x^5 + 24901/1440*x^4 - 20837/560*x^3 + 5869/140*x^2 - 18*x
9
3:
1/4320*x^9 - 7/720*x^8 + 31/180*x^7 - 401/240*x^6 + 13873/1440*x^5 - 4013/120*x^4 + 72569/1080*x^3 - 6289/90*x^2 + 28*x
9
4:
-1/2880*x^9 + 41/2880*x^8 - 353/1440*x^7 + 3313/1440*x^6 - 36769/2880*x^5 + 122249/2880*x^4 - 6519/80*x^3 + 6499/80*x^2 - 63/2*x
9
5:
1/2880*x^9 - 1/72*x^8 + 67/288*x^7 - 305/144*x^6 + 32773/2880*x^5 - 5273/144*x^4 + 1091/16*x^3 - 265/4*x^2 + 126/5*x
9
6:
-1/4320*x^9 + 13/1440*x^8 - 53/360*x^7 + 313/240*x^6 - 9823/1440*x^5 + 10279/480*x^4 - 84307/2160*x^3 + 6709/180*x^2 - 14*x
9
7:
1/10080*x^9 - 19/5040*x^8 + 151/2520*x^7 - 373/720*x^6 + 3817/1440*x^5 - 2939/360*x^4 + 4101/280*x^3 - 967/70*x^2 + 36/7*x
9
8:
-1/40320*x^9 + 37/40320*x^8 - 41/2880*x^7 + 347/2880*x^6 - 3487/5760*x^5 + 10579/5760*x^4 - 1823/560*x^3 + 3407/1120*x^2 - 9/8*x
9
9:
1/362880*x^9 - 1/10080*x^8 + 13/8640*x^7 - 1/80*x^6 + 1069/17280*x^5 - 89/480*x^4 + 29531/90720*x^3 - 761/2520*x^2 + 1/9*x
10
0:
1/3628800*x^10 - 11/725760*x^9 + 11/30240*x^8 - 121/24192*x^7 + 7513/172800*x^6 - 8591/34560*x^5 + 341693/362880*x^4 - 84095/36288*x^3 + 177133/50400*x^2 - 7381/2520*x + 1
10
1:
-1/362880*x^10 + 1/6720*x^9 - 211/60480*x^8 + 67/1440*x^7 - 6709/17280*x^6 + 6041/2880*x^5 - 663941/90720*x^4 + 79913/5040*x^3 - 4861/252*x^2 + 10*x
10
2:
1/80640*x^10 - 53/80640*x^9 + 607/40320*x^8 - 1123/5760*x^7 + 18047/11520*x^6 - 92771/11520*x^5 + 264767/10080*x^4 - 115923/2240*x^3 + 6121/112*x^2 - 45/2*x
10
3:
-1/30240*x^10 + 13/7560*x^9 - 97/2520*x^8 + 349/720*x^7 - 5419/1440*x^6 + 13349/720*x^5 - 433739/7560*x^4 + 400579/3780*x^3 - 6541/63*x^2 + 40*x
10
4:
1/17280*x^10 - 17/5760*x^9 + 31/480*x^8 - 2281/2880*x^7 + 34343/5760*x^6 - 163313/5760*x^5 + 728587/8640*x^4 - 71689/480*x^3 + 6751/48*x^2 - 105/2*x
10
5:
-1/14400*x^10 + 1/288*x^9 - 107/1440*x^8 + 8/9*x^7 - 93773/14400*x^6 + 43319/1440*x^5 - 62549/720*x^4 + 1197/8*x^3 - 6877/50*x^2 + 252/5*x
10
6:
1/17280*x^10 - 49/17280*x^9 + 19/320*x^8 - 1999/2880*x^7 + 28603/5760*x^6 - 129067/5760*x^5 + 273431/4320*x^4 - 461789/4320*x^3 + 6961/72*x^2 - 35*x
10
7:
-1/30240*x^10 + 1/630*x^9 - 41/1260*x^8 + 1877/5040*x^7 - 1253/480*x^6 + 8321/720*x^5 - 242639/7560*x^4 + 22439/420*x^3 - 1003/21*x^2 + 120/7*x
10
8:
1/80640*x^10 - 47/80640*x^9 + 59/5040*x^8 - 757/5760*x^7 + 10427/11520*x^6 - 45449/11520*x^5 + 435893/40320*x^4 - 39867/2240*x^3 + 3533/224*x^2 - 45/8*x
10
9:
-1/362880*x^10 + 23/181440*x^9 - 151/60480*x^8 + 119/4320*x^7 - 3229/17280*x^6 + 6947/8640*x^5 - 197741/90720*x^4 + 161353/45360*x^3 - 263/84*x^2 + 10/9*x
10
10:
1/3628800*x^10 - 1/80640*x^9 + 29/120960*x^8 - 1/384*x^7 + 3013/172800*x^6 - 19/256*x^5 + 4523/22680*x^4 - 1303/4032*x^3 + 7129/25200*x^2 - 1/10*x
11
0:
-1/39916800*x^11 + 1/604800*x^10 - 1/20736*x^9 + 11/13440*x^8 - 10831/1209600*x^7 + 1903/28800*x^6 - 242537/725760*x^5 + 139381/120960*x^4 - 341747/129600*x^3 + 190553/50400*x^2 - 83711/27720*x + 1
11
1:
1/3628800*x^11 - 13/725760*x^10 + 31/60480*x^9 - 1027/120960*x^8 + 15553/172800*x^7 - 22009/34560*x^6 + 1102859/362880*x^5 - 1748357/181440*x^4 + 325421/16800*x^3 - 55991/2520*x^2 + 11*x
11
2:
-1/725760*x^11 + 1/11340*x^10 - 599/241920*x^9 + 2423/60480*x^8 - 14251/34560*x^7 + 12137/4320*x^6 - 9261503/725760*x^5 + 6868181/181440*x^4 - 1397573/20160*x^3 + 69851/1008*x^2 - 55/2*x
11
3:
1/241920*x^11 - 1/3840*x^10 + 31/4320*x^9 - 4577/40320*x^8 + 13097/11520*x^7 - 28769/3840*x^6 + 3951097/120960*x^5 - 29483/320*x^4 + 685547/4320*x^3 - 74471/504*x^2 + 55*x
11
4:
-1/120960*x^11 + 31/60480*x^10 - 559/40320*x^9 + 4327/20160*x^8 - 805/384*x^7 + 12883/960*x^6 - 6846503/120960*x^5 + 9304859/60480*x^4 - 285363/1120*x^3 + 76781/336*x^2 - 165/2*x
11
5:
1/86400*x^11 - 61/86400*x^10 + 3/160*x^9 - 91/320*x^8 + 78191/28800*x^7 - 488231/28800*x^6 + 601607/8640*x^5 - 795769/4320*x^4 + 356683/1200*x^3 - 78167/300*x^2 + 462/5*x
11
6:
-1/86400*x^11 + 1/1440*x^10 - 313/17280*x^9 + 97/360*x^8 - 72581/28800*x^7 + 493/32*x^6 - 1070587/17280*x^5 + 115651/720*x^4 - 5497339/21600*x^3 + 79091/360*x^2 - 77*x
11
7:
1/120960*x^11 - 59/120960*x^10 + 1/80*x^9 - 409/2240*x^8 + 67607/40320*x^7 - 57991/5760*x^6 + 2407429/60480*x^5 - 3072931/30240*x^4 + 12709/80*x^3 - 11393/84*x^2 + 330/7*x
11
8:
-1/241920*x^11 + 29/120960*x^10 - 487/80640*x^9 + 3497/40320*x^8 - 1003/1280*x^7 + 8897/1920*x^6 - 4371359/241920*x^5 + 5512429/120960*x^4 - 473867/6720*x^3 + 40123/672*x^2 - 165/8*x
11
9:
1/725760*x^11 - 19/241920*x^10 + 353/181440*x^9 - 1109/40320*x^8 + 1693/6912*x^7 - 16471/11520*x^6 + 2000239/362880*x^5 - 832619/60480*x^4 + 1916903/90720*x^3 - 8959/504*x^2 + 55/9*x
11
10:
-1/3628800*x^11 + 1/64800*x^10 - 13/34560*x^9 + 317/60480*x^8 - 7963/172800*x^7 + 2873/10800*x^6 - 737251/725760*x^5 + 65237/25920*x^4 - 18421/4800*x^3 + 80939/25200*x^2 - 11/10*x
11
11:
1/39916800*x^11 - 1/725760*x^10 + 1/30240*x^9 - 11/24192*x^8 + 683/172800*x^7 - 781/34560*x^6 + 31063/362880*x^5 - 7645/36288*x^4 + 16103/50400*x^3 - 671/2520*x^2 + 1/11*x
12
0:
1/479001600*x^12 - 13/79833600*x^11 + 247/43545600*x^10 - 169/1451520*x^9 + 22711/14515200*x^8 - 3887/268800*x^7 + 4090021/43545600*x^6 - 124891/290304*x^5 + 14936519/10886400*x^4 - 5356117/1814400*x^3 + 1676701/415800*x^2 - 86021/27720*x + 1
12
1:
-1/39916800*x^12 + 1/518400*x^11 - 1/15120*x^10 + 23/17280*x^9 - 21101/1209600*x^8 + 26971/172800*x^7 - 352363/362880*x^6 + 108643/25920*x^5 - 1855669/151200*x^4 + 5209/225*x^3 - 58301/2310*x^2 + 12*x
12
2:
1/7257600*x^12 - 19/1814400*x^11 + 19/53760*x^10 - 211/30240*x^9 + 216061/2419200*x^8 - 67027/86400*x^7 + 6745939/1451520*x^6 - 3465269/181440*x^5 + 31665443/604800*x^4 - 2270987/25200*x^3 + 72161/840*x^2 - 33*x
12
3:
-1/2177280*x^12 + 5/145152*x^11 - 89/77760*x^10 + 2683/120960*x^9 - 201527/725760*x^8 + 81157/34560*x^7 - 14825779/1088640*x^6 + 9759623/181440*x^5 - 5461793/38880*x^4 + 71822/315*x^3 - 76781/378*x^2 + 220/3*x
12
4:
1/967680*x^12 - 37/483840*x^11 + 269/107520*x^10 - 7681/161280*x^9 + 62791/107520*x^8 - 37033/7680*x^7 + 26325599/967680*x^6 - 50383877/483840*x^5 + 4235597/16128*x^4 - 5520439/13440*x^3 + 79091/224*x^2 - 495/4*x
12
5:
-1/604800*x^12 + 73/604800*x^11 - 7/1800*x^10 + 163/2240*x^9 - 176471/201600*x^8 + 203789/28800*x^7 - 11796193/302400*x^6 + 4405411/30240*x^5 - 1289677/3600*x^4 + 287054/525*x^3 - 80477/175*x^2 + 792/5*x
12
6:
1/518400*x^12 - 1/7200*x^11 + 457/103680*x^10 - 701/8640*x^9 + 165701/172800*x^8 - 27389/3600*x^7 + 4265227/103680*x^6 - 433963/2880*x^5 + 47131699/129600*x^4 - 2946397/5400*x^3 + 81401/180*x^2 - 154*x
12
7:
-1/604800*x^12 + 71/604800*x^11 - 37/10080*x^10 + 149/2240*x^9 - 155951/201600*x^8 + 1217221/201600*x^7 - 1942859/60480*x^6 + 3503501/30240*x^5 - 6946529/25200*x^4 + 214408/525*x^3 - 11723/35*x^2 + 792/7*x
12
8:
1/967680*x^12 - 1/13824*x^11 + 719/322560*x^10 - 917/23040*x^9 + 49039/107520*x^8 - 26951/7680*x^7 + 17823623/967680*x^6 - 4534369/69120*x^5 + 12446459/80640*x^4 - 434831/1920*x^3 + 20639/112*x^2 - 495/8*x
12
9:
-1/2177280*x^12 + 23/725760*x^11 - 131/136080*x^10 + 6151/362880*x^9 - 139103/725760*x^8 + 16777/11520*x^7 - 8226277/1088640*x^6 + 4833097/181440*x^5 - 3380809/54432*x^4 + 256411/2835*x^3 - 27647/378*x^2 + 220/9*x
12
10:
1/7257600*x^12 - 17/1814400*x^11 + 97/345600*x^10 - 59/12096*x^9 + 131821/2419200*x^8 - 35381/86400*x^7 + 15270191/7257600*x^6 - 667103/90720*x^5 + 1470529/86400*x^4 - 620731/25200*x^3 + 83249/4200*x^2 - 33/5*x
12
11:
-1/39916800*x^12 + 67/39916800*x^11 - 1/20160*x^10 + 103/120960*x^9 - 11381/1209600*x^8 + 12101/172800*x^7 - 129469/362880*x^6 + 224603/181440*x^5 - 430559/151200*x^4 + 6458/1575*x^3 - 7591/2310*x^2 + 12/11*x
12
12:
1/479001600*x^12 - 1/7257600*x^11 + 1/248832*x^10 - 11/161280*x^9 + 10831/14515200*x^8 - 1903/345600*x^7 + 242537/8709120*x^6 - 139381/1451520*x^5 + 341747/1555200*x^4 - 190553/604800*x^3 + 83711/332640*x^2 - 1/12*x
13
0:
-1/6227020800*x^13 + 1/68428800*x^12 - 41/68428800*x^11 + 91/6220800*x^10 - 491/2073600*x^9 + 5551/2073600*x^8 - 944311/43545600*x^7 + 790153/6220800*x^6 - 1666393/3110400*x^5 + 2486939/1555200*x^4 - 9301169/2851200*x^3 + 63427/14850*x^2 - 1145993/360360*x + 1
13
1:
1/479001600*x^13 - 1/5322240*x^12 + 331/43545600*x^11 - 53/290304*x^10 + 42031/14515200*x^9 - 15437/483840*x^8 + 10886713/43545600*x^7 - 677969/483840*x^6 + 60566579/10886400*x^5 - 5524829/362880*x^4 + 11302933/415800*x^3 - 785633/27720*x^2 + 13*x
13
2:
-1/79833600*x^13 + 89/79833600*x^12 - 323/7257600*x^11 + 509/483840*x^10 - 4399/268800*x^9 + 425959/2419200*x^8 - 9720289/7257600*x^7 + 10492669/1451520*x^6 - 49589209/1814400*x^5 + 42377677/604800*x^4 - 31687661/277200*x^3 + 965813/9240*x^2 - 39*x
13
3:
1/21772800*x^13 - 11/2721600*x^12 + 3467/21772800*x^11 - 8069/2177280*x^10 + 410801/7257600*x^9 - 1081037/1814400*x^8 + 96119141/21772800*x^7 - 50258573/2177280*x^6 + 457090399/5443200*x^5 - 559077371/2721600*x^4 + 5986021/18900*x^3 - 1025873/3780*x^2 + 286/3*x
13
4:
-1/8709120*x^13 + 29/2903040*x^12 - 3383/8709120*x^11 + 25853/2903040*x^10 - 388079/2903040*x^9 + 9887/7168*x^8 - 86985653/8709120*x^7 + 147666847/2903040*x^6 - 782058311/4354560*x^5 + 308436439/725760*x^4 - 76511167/120960*x^3 + 1055903/2016*x^2 - 715/4*x
13
5:
1/4838400*x^13 - 43/2419200*x^12 + 3301/4838400*x^11 - 12431/806400*x^10 + 367181/1612800*x^9 - 1860323/806400*x^8 + 79226783/4838400*x^7 - 197404619/2419200*x^6 + 340518149/1209600*x^5 - 131139199/201600*x^4 + 3973133/4200*x^3 - 1073921/1400*x^2 + 1287/5*x
13
6:
-1/3628800*x^13 + 17/725760*x^12 - 3221/3628800*x^11 + 14353/725760*x^10 - 115987/403200*x^9 + 693757/241920*x^8 - 72598343/3628800*x^7 + 71070619/725760*x^6 - 150500027/453600*x^5 + 136685123/181440*x^4 - 40745191/37800*x^3 + 1085933/1260*x^2 - 286*x
13
7:
1/3628800*x^13 - 1/43200*x^12 + 449/518400*x^11 - 329/17280*x^10 + 47183/172800*x^9 - 19313/7200*x^8 + 66900209/3628800*x^7 - 1536389/17280*x^6 + 38486677/129600*x^5 - 14370923/21600*x^4 + 423307/450*x^3 - 22337/30*x^2 + 1716/7*x
13
8:
-1/4838400*x^13 + 83/4838400*x^12 - 3067/4838400*x^11 + 493/35840*x^10 - 314011/1612800*x^9 + 1014821/537600*x^8 - 61969361/4838400*x^7 + 59037653/967680*x^6 - 487306333/2419200*x^5 + 180066869/403200*x^4 - 42046301/67200*x^3 + 275237/560*x^2 - 1287/8*x
13
9:
1/8709120*x^13 - 41/4354560*x^12 + 2993/8709120*x^11 - 32077/4354560*x^10 + 299029/2903040*x^9 - 286529/290304*x^8 + 57673643/8709120*x^7 - 135940183/4354560*x^6 + 222298873/2177280*x^5 - 244368041/1088640*x^4 + 7081391/22680*x^3 - 368651/1512*x^2 + 715/9*x
13
10:
-1/21772800*x^13 + 1/268800*x^12 - 2921/21772800*x^11 + 20627/7257600*x^10 - 285221/7257600*x^9 + 901447/2419200*x^8 - 53906243/21772800*x^7 + 27986747/2419200*x^6 - 204327889/5443200*x^5 + 148715683/1814400*x^4 - 8568997/75600*x^3 + 1109957/12600*x^2 - 143/5*x
13
11:
1/79833600*x^13 - 1/997920*x^12 + 2851/79833600*x^11 - 181/241920*x^10 + 8257/806400*x^9 - 11633/120960*x^8 + 4598263/7257600*x^7 - 2132303/725760*x^6 + 17182549/1814400*x^5 - 1243447/60480*x^4 + 1960853/69300*x^3 - 101203/4620*x^2 + 78/11*x
13
12:
-1/479001600*x^13 + 79/479001600*x^12 - 253/43545600*x^11 + 1049/8709120*x^10 - 23701/14515200*x^9 + 220729/14515200*x^8 - 4329799/43545600*x^7 + 3989267/8709120*x^6 - 31963753/21772800*x^5 + 34528931/10886400*x^4 - 28923299/6652800*x^3 + 1115963/332640*x^2 - 13/12*x
13
13:
1/6227020800*x^13 - 1/79833600*x^12 + 19/43545600*x^11 - 13/1451520*x^10 + 1747/14515200*x^9 - 299/268800*x^8 + 314617/43545600*x^7 - 9607/290304*x^6 + 1148963/10886400*x^5 - 412009/1814400*x^4 + 128977/415800*x^3 - 6617/27720*x^2 + 1/13*x
14
0:
1/87178291200*x^14 - 1/830269440*x^13 + 1/17418240*x^12 - 1/608256*x^11 + 2747/87091200*x^10 - 71/165888*x^9 + 515261/121927680*x^8 - 35717/1161216*x^7 + 899683/5443200*x^6 - 22463/34560*x^5 + 21939781/11975040*x^4 - 406841/114048*x^3 + 30946717/6879600*x^2 - 1171733/360360*x + 1
14
1:
-1/6227020800*x^14 + 1/59875200*x^13 - 377/479001600*x^12 + 121/5443200*x^11 - 2029/4838400*x^10 + 10111/1814400*x^9 - 2333641/43545600*x^8 + 2052223/5443200*x^7 - 10543339/5443200*x^6 + 4873447/680400*x^5 - 184486889/9979200*x^4 + 13078889/415800*x^3 - 811373/25740*x^2 + 14*x
14
2:
1/958003200*x^14 - 103/958003200*x^13 + 4799/958003200*x^12 - 12157/87091200*x^11 + 75221/29030400*x^10 - 980233/29030400*x^9 + 27610567/87091200*x^8 - 188547391/87091200*x^7 + 466421833/43545600*x^6 - 821381957/21772800*x^5 + 3643333061/39916800*x^4 - 118150411/831600*x^3 + 991553/7920*x^2 - 91/2*x
14
3:
-1/239500800*x^14 + 17/39916800*x^13 - 4699/239500800*x^12 + 979/1814400*x^11 - 214733/21772800*x^10 + 152657/1209600*x^9 - 25248487/21772800*x^8 + 7000961/907200*x^7 - 100733657/2721600*x^6 + 28475077/226800*x^5 - 4344535109/14968800*x^4 + 29644553/69300*x^3 - 1051613/2970*x^2 + 364/3*x
14
4:
1/87091200*x^14 - 101/87091200*x^13 + 4601/87091200*x^12 - 124921/87091200*x^11 + 250007/9676800*x^10 - 9437341/29030400*x^9 + 255163523/87091200*x^8 - 1660799683/87091200*x^7 + 1941531049/21772800*x^6 - 3199858747/10886400*x^5 + 1194294287/1814400*x^4 - 567255259/604800*x^3 + 1081643/1440*x^2 - 1001/4*x
14
5:
-1/43545600*x^14 + 1/435456*x^13 - 901/8709120*x^12 + 151/54432*x^11 - 715249/14515200*x^10 + 443059/725760*x^9 - 47098783/8709120*x^8 + 7519921/217728*x^7 - 861175241/5443200*x^6 + 17356529/34020*x^5 - 202665917/181440*x^4 + 2353825/1512*x^3 - 1099661/900*x^2 + 2002/5*x
14
6:
1/29030400*x^14 - 11/3225600*x^13 + 4411/29030400*x^12 - 38953/9676800*x^11 + 2048593/29030400*x^10 - 8340239/9676800*x^9 + 218287313/29030400*x^8 - 16934937/358400*x^7 + 3089471773/14515200*x^6 - 1632475457/2419200*x^5 + 5272921597/3628800*x^4 - 75376333/37800*x^3 + 1111673/720*x^2 - 1001/2*x
14
7:
-1/25401600*x^14 + 1/259200*x^13 - 617/3628800*x^12 + 577/129600*x^11 - 31081/403200*x^10 + 80291/86400*x^9 - 203172737/25401600*x^8 + 22486511/453600*x^7 - 99903761/453600*x^6 + 11161411/16200*x^5 - 110755829/75600*x^4 + 894479/450*x^3 - 1120253/735*x^2 + 3432/7*x
14
8:
1/29030400*x^14 - 97/29030400*x^13 + 4229/29030400*x^12 - 109493/29030400*x^11 + 624601/9676800*x^10 - 7440617/9676800*x^9 + 189836807/29030400*x^8 - 1162759319/29030400*x^7 + 638406047/3628800*x^6 - 1975672469/3628800*x^5 + 693303493/604800*x^4 - 310838327/201600*x^3 + 35209/30*x^2 - 3003/8*x
14
9:
-1/43545600*x^14 + 1/453600*x^13 - 4141/43545600*x^12 + 491/201600*x^11 - 1795243/43545600*x^10 + 440731/907200*x^9 - 178015823/43545600*x^8 + 44971307/1814400*x^7 - 586940077/5443200*x^6 + 25006391/75600*x^5 - 1880529671/2721600*x^4 + 104669239/113400*x^3 - 377231/540*x^2 + 2002/9*x
14
10:
1/87091200*x^14 - 19/17418240*x^13 + 811/17418240*x^12 - 4111/3483648*x^11 + 191333/9676800*x^10 - 1339487/5806080*x^9 + 33497713/17418240*x^8 - 40262725/3483648*x^7 + 2171820839/43545600*x^6 - 661347499/4354560*x^5 + 228767549/725760*x^4 - 1266257/3024*x^3 + 1135697/3600*x^2 - 1001/10*x
14
11:
-1/239500800*x^14 + 47/119750400*x^13 - 361/21772800*x^12 + 24911/59875200*x^11 - 50111/7257600*x^10 + 289727/3628800*x^9 - 14369983/21772800*x^8 + 10712339/2721600*x^7 - 45906577/2721600*x^6 + 34732387/680400*x^5 - 525787567/4989600*x^4 + 28969987/207900*x^3 - 9413/90*x^2 + 364/11*x
14
12:
1/958003200*x^14 - 31/319334400*x^13 + 3889/958003200*x^12 - 2929/29030400*x^11 + 144533/87091200*x^10 - 184181/9676800*x^9 + 13600417/87091200*x^8 - 26854507/29030400*x^7 + 85794049/21772800*x^6 - 43045867/3628800*x^5 + 1459518689/59875200*x^4 - 213622723/6652800*x^3 + 1141703/47520*x^2 - 91/12*x
14
13:
-1/6227020800*x^14 + 23/1556755200*x^13 - 293/479001600*x^12 + 41/2721600*x^11 - 1189/4838400*x^10 + 10151/3628800*x^9 - 992749/43545600*x^8 + 730711/5443200*x^7 - 3096319/5443200*x^6 + 579923/340200*x^5 - 34820141/9979200*x^4 + 1904933/415800*x^3 - 88001/25740*x^2 + 14/13*x
14
14:
1/87178291200*x^14 - 1/958003200*x^13 + 41/958003200*x^12 - 13/12441600*x^11 + 491/29030400*x^10 - 793/4147200*x^9 + 944311/609638400*x^8 - 112879/12441600*x^7 + 1666393/43545600*x^6 - 355277/3110400*x^5 + 9301169/39916800*x^4 - 9061/29700*x^3 + 1145993/5045040*x^2 - 1/14*x
15
0:
-1/1307674368000*x^15 + 1/10897286400*x^14 - 47/9340531200*x^13 + 1/5987520*x^12 - 26921/7185024000*x^11 + 109/1814400*x^10 - 324509/457228800*x^9 + 4783/762048*x^8 - 54576553/1306368000*x^7 + 2271089/10886400*x^6 - 277382447/359251200*x^5 + 2065639/997920*x^4 - 35118025721/9081072000*x^3 + 13215487/2802800*x^2 - 1195757/360360*x + 1
15
1:
1/87178291200*x^15 - 17/12454041600*x^14 + 71/958003200*x^13 - 2329/958003200*x^12 + 223/4147200*x^11 - 24599/29030400*x^10 + 5973601/609638400*x^9 - 7346057/87091200*x^8 + 1475953/2721600*x^7 - 28162523/10886400*x^6 + 8548607/950400*x^5 - 146723651/6652800*x^4 + 60461593/1681680*x^3 - 835397/24024*x^2 + 15*x
15
2:
-1/12454041600*x^15 + 59/6227020800*x^14 - 61/119750400*x^13 + 989/59875200*x^12 - 5231/14515200*x^11 + 40549/7257600*x^10 - 1379251/21772800*x^9 + 5795249/10886400*x^8 - 289311887/87091200*x^7 + 664545493/43545600*x^6 - 149466307/2956800*x^5 + 1546697837/13305600*x^4 - 20848547/120120*x^3 + 1015577/6864*x^2 - 105/2*x
15
3:
1/2874009600*x^15 - 13/319334400*x^14 + 6229/2874009600*x^13 - 66571/958003200*x^12 + 390953/261273600*x^11 - 1989607/87091200*x^10 + 66465877/261273600*x^9 - 60750041/29030400*x^8 + 207888451/16329600*x^7 - 617568593/10886400*x^6 + 32534861339/179625600*x^5 - 23857083361/59875200*x^4 + 281523559/498960*x^3 - 1075637/2376*x^2 + 455/3*x
15
4:
-1/958003200*x^15 + 29/239500800*x^14 - 139/21772800*x^13 + 12121/59875200*x^12 - 62483/14515200*x^11 + 235087/3628800*x^10 - 15450997/21772800*x^9 + 31183253/5443200*x^8 - 2970738131/87091200*x^7 + 3229334839/21772800*x^6 - 6129294103/13305600*x^5 + 3269363347/3326400*x^4 - 18107311/13440*x^3 + 1105667/1056*x^2 - 1365/4*x
15
5:
1/435456000*x^15 - 23/87091200*x^14 + 1201/87091200*x^13 - 1507/3483648*x^12 + 1319249/145152000*x^11 - 3917983/29030400*x^10 + 126849403/87091200*x^9 - 201455717/17418240*x^8 + 230071601/3402000*x^7 - 3138934651/10886400*x^6 + 176798693/201600*x^5 - 221496517/120960*x^4 + 103207793/42000*x^3 - 224737/120*x^2 + 3003/5*x
15
6:
-1/261273600*x^15 + 19/43545600*x^14 - 737/32659200*x^13 + 1271/1814400*x^12 - 1900739/130636800*x^11 + 4645801/21772800*x^10 - 21199931/9331200*x^9 + 193584983/10886400*x^8 - 26754892001/261273600*x^7 + 2079145531/4838400*x^6 - 84007238759/65318400*x^5 + 28776650641/10886400*x^4 - 158534377/45360*x^3 + 1135697/432*x^2 - 5005/6*x
15
7:
1/203212800*x^15 - 113/203212800*x^14 + 827/29030400*x^13 - 25411/29030400*x^12 + 174023/9676800*x^11 - 2522719/9676800*x^10 + 557256047/203212800*x^9 - 4306835671/203212800*x^8 + 218600713/1814400*x^7 - 1811075923/3628800*x^6 + 297351533/201600*x^5 - 603869969/201600*x^4 + 15356659/3920*x^3 - 1144277/392*x^2 + 6435/7*x
15
8:
-1/203212800*x^15 + 1/1814400*x^14 - 29/1036800*x^13 + 193/226800*x^12 - 83719/4838400*x^11 + 75043/302400*x^10 - 131166143/50803200*x^9 + 2237897/113400*x^8 - 460176289/4147200*x^7 + 825125941/1814400*x^6 - 178809037/134400*x^5 + 33726391/12600*x^4 - 108870653/31360*x^3 + 143839/56*x^2 - 6435/8*x
15
9:
1/261273600*x^15 - 37/87091200*x^14 + 5581/261273600*x^13 - 56057/87091200*x^12 + 3386083/261273600*x^11 - 1780879/9676800*x^10 + 495342143/261273600*x^9 - 1249849571/87091200*x^8 + 652662223/8164800*x^7 - 3534853769/10886400*x^6 + 15383980811/16329600*x^5 - 3413334089/1814400*x^4 + 109950473/45360*x^3 - 128413/72*x^2 + 5005/9*x
15
10:
-1/435456000*x^15 + 11/43545600*x^14 - 137/10886400*x^13 + 409/1088640*x^12 - 543937/72576000*x^11 + 765371/7257600*x^10 - 23443657/21772800*x^9 + 17594483/2177280*x^8 - 19442163553/435456000*x^7 + 1567631503/8709120*x^6 - 1254757531/2419200*x^5 + 249027661/241920*x^4 - 13852667/10500*x^3 + 1159721/1200*x^2 - 3003/10*x
15
11:
1/958003200*x^15 - 109/958003200*x^14 + 5381/958003200*x^13 - 159209/958003200*x^12 + 1049441/319334400*x^11 - 1331119/29030400*x^10 + 40445413/87091200*x^9 - 301248457/87091200*x^8 + 103295831/5443200*x^7 - 827528203/10886400*x^6 + 160975931/739200*x^5 - 2860697731/6652800*x^4 + 10139863/18480*x^3 - 105727/264*x^2 + 1365/11*x
15
12:
-1/2874009600*x^15 + 1/26611200*x^14 - 1321/718502400*x^13 + 3229/59875200*x^12 - 138169/130636800*x^11 + 159401/10886400*x^10 - 9616213/65318400*x^9 + 1976179/1814400*x^8 - 1551629011/261273600*x^7 + 515061979/21772800*x^6 - 24226741543/359251200*x^5 + 3969230807/29937600*x^4 - 672835853/3991680*x^3 + 1165727/9504*x^2 - 455/12*x
15
13:
1/12454041600*x^15 - 107/12454041600*x^14 + 5189/12454041600*x^13 - 11611/958003200*x^12 + 6847/29030400*x^11 - 94109/29030400*x^10 + 402847/12441600*x^9 - 20736923/87091200*x^8 + 1757123/1360800*x^7 - 55723553/10886400*x^6 + 96662087/6652800*x^5 - 189340169/6652800*x^4 + 8665381/240240*x^3 - 89849/3432*x^2 + 105/13*x
15
14:
-1/87178291200*x^15 + 53/43589145600*x^14 - 1/17107200*x^13 + 101/59875200*x^12 - 473/14515200*x^11 + 3229/7257600*x^10 - 673219/152409600*x^9 + 2461967/76204800*x^8 - 15185081/87091200*x^7 + 29969773/43545600*x^6 - 17264887/8870400*x^5 + 50565173/13305600*x^4 - 8077807/1681680*x^3 + 1170017/336336*x^2 - 15/14*x
15
15:
1/1307674368000*x^15 - 1/12454041600*x^14 + 1/261273600*x^13 - 1/9123840*x^12 + 2747/1306368000*x^11 - 71/2488320*x^10 + 515261/1828915200*x^9 - 35717/17418240*x^8 + 899683/81648000*x^7 - 22463/518400*x^6 + 21939781/179625600*x^5 - 406841/1710720*x^4 + 30946717/103194000*x^3 - 1171733/5405400*x^2 + 1/15*x
16
0:
1/20922789888000*x^16 - 17/2615348736000*x^15 + 17/41845579776*x^14 - 289/18681062400*x^13 + 46121/114960384000*x^12 - 107797/14370048000*x^11 + 763997/7315660800*x^10 - 1007743/914457600*x^9 + 1300371871/146313216000*x^8 - 143219441/2612736000*x^7 + 1476517439/5748019200*x^6 - 647718649/718502400*x^5 + 37319451569/16144128000*x^4 - 75588323677/18162144000*x^3 + 993366559/201801600*x^2 - 2436559/720720*x + 1
16
1:
-1/1307674368000*x^16 + 1/9686476800*x^15 - 239/37362124800*x^14 + 1/4147200*x^13 - 88777/14370048000*x^12 + 661/5806080*x^11 - 2847773/1828915200*x^10 + 362963/22579200*x^9 - 10297963/81648000*x^8 + 389281/518400*x^7 - 603372853/179625600*x^6 + 220833527/19958400*x^5 - 29424476167/1135134000*x^4 + 15543383/382200*x^3 - 1715839/45045*x^2 + 16*x
16
2:
1/174356582400*x^16 - 67/87178291200*x^15 + 7/148262400*x^14 - 211/119750400*x^13 + 8549/191600640*x^12 - 11771/14515200*x^11 + 3325603/304819200*x^10 - 16829257/152409600*x^9 + 49100179/58060800*x^8 - 425577227/87091200*x^7 + 10083824893/479001600*x^6 - 1758324563/26611200*x^5 + 21983441111/151351200*x^4 - 702698699/3363360*x^3 + 2076199/12012*x^2 - 60*x
16
3:
-1/37362124800*x^16 + 19/5337446400*x^15 - 8101/37362124800*x^14 + 23029/2874009600*x^13 - 576607/2874009600*x^12 + 940313/261273600*x^11 - 12459001/261273600*x^10 + 123861877/261273600*x^9 - 2902457/816480*x^8 + 654241247/32659200*x^7 - 15044074607/179625600*x^6 + 45548387039/179625600*x^5 - 7419574301/13899600*x^4 + 2365130357/3243240*x^3 - 2196319/3861*x^2 + 560/3*x
16
4:
1/11496038400*x^16 - 1/87091200*x^15 + 1993/2874009600*x^14 - 6079/239500800*x^13 + 3613427/5748019200*x^12 - 53891/4838400*x^11 + 38019349/261273600*x^10 - 30995747/21772800*x^9 + 10953650899/1045094400*x^8 - 5037429121/87091200*x^7 + 339345112759/1437004800*x^6 - 2526049069/3628800*x^5 + 113582746049/79833600*x^4 - 278473343/147840*x^3 + 2256379/1584*x^2 - 455*x
16
5:
-1/4790016000*x^16 + 131/4790016000*x^15 - 523/319334400*x^14 + 56891/958003200*x^13 - 6971747/4790016000*x^12 + 3699809/145152000*x^11 - 28628417/87091200*x^10 + 276079003/87091200*x^9 - 208392901/9072000*x^8 + 6781182101/54432000*x^7 - 29885041919/59875200*x^6 + 9593819849/6652800*x^5 - 12003695987/4158000*x^4 + 864991319/231000*x^3 - 458483/165*x^2 + 4368/5*x
16
6:
1/2612736000*x^16 - 13/261273600*x^15 + 193/65318400*x^14 - 3467/32659200*x^13 + 3364931/1306368000*x^12 - 5828663/130636800*x^11 + 74279593/130636800*x^10 - 353590217/65318400*x^9 + 101091525473/2612736000*x^8 - 54035213069/261273600*x^7 + 106620534691/130636800*x^6 - 151677572399/65318400*x^5 + 3894333287/850500*x^4 - 2655798217/453600*x^3 + 2316439/540*x^2 - 4004/3*x
16
7:
-1/1828915200*x^16 + 43/609638400*x^15 - 7597/1828915200*x^14 + 12881/87091200*x^13 - 185729/52254720*x^12 + 1769029/29030400*x^11 - 1404889631/1828915200*x^10 + 4407644141/609638400*x^9 - 2918520331/57153600*x^8 + 419347559/1555200*x^7 - 17164771181/16329600*x^6 + 5361494497/1814400*x^5 - 9145229221/1587600*x^4 + 14286073/1960*x^3 - 2333599/441*x^2 + 11440/7*x
16
8:
1/1625702400*x^16 - 1/12700800*x^15 + 89/19353600*x^14 - 589/3628800*x^13 + 448789/116121600*x^12 - 79381/1209600*x^11 + 332881727/406425600*x^10 - 193827259/25401600*x^9 + 825844009/15482880*x^8 - 1011589991/3628800*x^7 + 31231874111/29030400*x^6 - 603879893/201600*x^5 + 65336872057/11289600*x^4 - 56952509/7840*x^3 + 2346469/448*x^2 - 6435/4*x
16
9:
-1/1828915200*x^16 + 127/1828915200*x^15 - 1051/261273600*x^14 + 36781/261273600*x^13 - 868117/261273600*x^12 + 14608723/261273600*x^11 - 1264681871/1828915200*x^10 + 11675023001/1828915200*x^9 - 722124737/16329600*x^8 + 7482134797/32659200*x^7 - 14317210181/16329600*x^6 + 39551957111/16329600*x^5 - 7376420543/1587600*x^4 + 920053879/158760*x^3 - 87277/21*x^2 + 11440/9*x
16
10:
1/2612736000*x^16 - 1/20736000*x^15 + 181/65318400*x^14 - 349/3628800*x^13 + 2940611/1306368000*x^12 - 2726117/72576000*x^11 + 12036293/26127360*x^10 - 30613519/7257600*x^9 + 75744509153/2612736000*x^8 - 21636455111/145152000*x^7 + 73998077899/130636800*x^6 - 11283198553/7257600*x^5 + 960626791/324000*x^4 - 309053641/84000*x^3 + 2364487/900*x^2 - 4004/5*x
16
11:
-1/4790016000*x^16 + 1/38320128*x^15 - 19/12773376*x^14 + 49061/958003200*x^13 - 5695667/4790016000*x^12 + 6286673/319334400*x^11 - 834713/3483648*x^10 + 189675013/87091200*x^9 - 4214003/283500*x^8 + 826598959/10886400*x^7 - 3434461291/11975040*x^6 + 5208246359/6652800*x^5 - 6177689297/4158000*x^4 + 84819349/46200*x^3 - 215549/165*x^2 + 4368/11*x
16
12:
1/11496038400*x^16 - 31/2874009600*x^15 + 1753/2874009600*x^14 - 1361/65318400*x^13 + 551959/1149603840*x^12 - 1030879/130636800*x^11 + 24918709/261273600*x^10 - 56250463/65318400*x^9 + 6104745427/1045094400*x^8 - 7751701981/261273600*x^7 + 160203103999/1437004800*x^6 - 108814658593/359251200*x^5 + 137107923619/239500800*x^4 - 255794977/362880*x^3 + 2376499/4752*x^2 - 455/3*x
16
13:
-1/37362124800*x^16 + 41/12454041600*x^15 - 6901/37362124800*x^14 + 77989/12454041600*x^13 - 411727/2874009600*x^12 + 7543/3225600*x^11 - 7337161/261273600*x^10 + 21951929/87091200*x^9 - 5553083/3265920*x^8 + 93545099/10886400*x^7 - 5773631447/179625600*x^6 + 1735933561/19958400*x^5 - 5312786539/32432400*x^4 + 24155921/120120*x^3 - 183163/1287*x^2 + 560/13*x
16
14:
1/174356582400*x^16 - 61/87178291200*x^15 + 283/7264857600*x^14 - 157/119750400*x^13 + 28537/958003200*x^12 - 7013/14515200*x^11 + 1758163/304819200*x^10 - 7847719/152409600*x^9 + 140475781/406425600*x^8 - 151450421/87091200*x^7 + 3103491973/479001600*x^6 - 464922461/26611200*x^5 + 2482466029/75675600*x^4 - 135094997/3363360*x^3 + 2385079/84084*x^2 - 60/7*x
16
15:
-1/1307674368000*x^16 + 11/118879488000*x^15 - 191/37362124800*x^14 + 491/2874009600*x^13 - 55417/14370048000*x^12 + 81227/1306368000*x^11 - 1350221/1828915200*x^10 + 11994461/1828915200*x^9 - 1789229/40824000*x^8 + 35865701/163296000*x^7 - 146474653/179625600*x^6 + 35795891/16329600*x^5 - 13979127511/3405402000*x^4 + 2846343061/567567000*x^3 - 2388511/675675*x^2 + 16/15*x
16
16:
1/20922789888000*x^16 - 1/174356582400*x^15 + 47/149448499200*x^14 - 1/95800320*x^13 + 26921/114960384000*x^12 - 109/29030400*x^11 + 324509/7315660800*x^10 - 4783/12192768*x^9 + 54576553/20901888000*x^8 - 2271089/174182400*x^7 + 277382447/5748019200*x^6 - 2065639/15966720*x^5 + 35118025721/145297152000*x^4 - 13215487/44844800*x^3 + 1195757/5765760*x^2 - 1/16*x
17
0:
-1/355687428096000*x^17 + 1/2324754432000*x^16 - 53/1743565824000*x^15 + 17/12915302400*x^14 - 19463/498161664000*x^13 + 3587/4257792000*x^12 - 5490071/402361344000*x^11 + 137581/812851200*x^10 - 79243781/48771072000*x^9 + 7292813/602112000*x^8 - 334947281/4790016000*x^7 + 13195009/42577920*x^6 - 1356664151597/1307674368000*x^5 + 371446039969/145297152000*x^4 - 80847323107/18162144000*x^3 + 344499373/67267200*x^2 - 42142223/12252240*x + 1
17
1:
1/20922789888000*x^17 - 19/2615348736000*x^16 + 41/80472268800*x^15 - 817/37362124800*x^14 + 73841/114960384000*x^13 - 14041/1026432000*x^12 + 1596857/7315660800*x^11 - 4863259/1828915200*x^10 + 3652372111/146313216000*x^9 - 472754257/2612736000*x^8 + 5792865167/5748019200*x^7 - 437315723/102643200*x^6 + 1943543140681/145297152000*x^5 - 546379942349/18162144000*x^4 + 707713291/15523200*x^3 - 29889983/720720*x^2 + 17*x
17
2:
-1/2615348736000*x^17 + 151/2615348736000*x^16 - 1051/261534873600*x^15 + 1597/9340531200*x^14 - 71441/14370048000*x^13 + 214793/2052864000*x^12 - 150557/91445760*x^11 + 18038753/914457600*x^10 - 3319882711/18289152000*x^9 + 479323369/373248000*x^8 - 19950118247/2874009600*x^7 + 5802139009/205286400*x^6 - 1023954385579/12108096000*x^5 + 202669970171/1135134000*x^4 - 12527213603/50450400*x^3 + 36016103/180180*x^2 - 68*x
17
3:
1/523069747200*x^17 - 1/3487131648*x^16 + 157/7925299200*x^15 - 3469/4151347200*x^14 + 461/19160064*x^13 - 22841/45619200*x^12 + 14222161/1828915200*x^11 - 55944149/609638400*x^10 + 1011479383/1219276800*x^9 - 41712889/7257600*x^8 + 7258631543/239500800*x^7 - 341607319/2851200*x^6 + 1028425638017/2971987200*x^5 - 953883252529/1362160800*x^4 + 42052124029/45405360*x^3 - 38058143/54054*x^2 + 680/3*x
17
4:
-1/149448499200*x^17 + 149/149448499200*x^16 - 1277/18681062400*x^15 + 106829/37362124800*x^14 - 42613/522547200*x^13 + 9650059/5748019200*x^12 - 6730099/261273600*x^11 + 11189867/37324800*x^10 - 2788167727/1045094400*x^9 + 3794787919/209018880*x^8 - 269591381723/2874009600*x^7 + 520706334479/1437004800*x^6 - 211665019571/207567360*x^5 + 2081282288053/1037836800*x^4 - 1348538783/524160*x^3 + 39079163/20592*x^2 - 595*x
17
5:
1/57480192000*x^17 - 37/14370048000*x^16 + 1259/7185024000*x^15 - 20891/2874009600*x^14 + 5903741/28740096000*x^13 - 60153349/14370048000*x^12 + 41479043/653184000*x^11 - 190690523/261273600*x^10 + 33469574503/5225472000*x^9 - 28037258003/653184000*x^8 + 1566931472077/7185024000*x^7 - 1160918147/1403325*x^6 + 303834751687/133056000*x^5 - 31376096503/7128000*x^4 + 15346728623/2772000*x^3 - 1587671/396*x^2 + 6188/5*x
17
6:
-1/28740096000*x^17 + 7/1368576000*x^16 - 331/958003200*x^15 + 227/15966720*x^14 - 1907497/4790016000*x^13 + 12832273/1596672000*x^12 - 985039/8164800*x^11 + 11938991/8709120*x^10 - 10349481001/870912000*x^9 + 22817253169/290304000*x^8 - 75455979437/191600640*x^7 + 47020094101/31933440*x^6 - 14388017636123/3592512000*x^5 + 569466300287/74844000*x^4 - 47094378449/4989600*x^3 + 40100183/5940*x^2 - 6188/3*x
17
7:
1/18289152000*x^17 - 73/9144576000*x^16 + 979/1828915200*x^15 - 7993/365783040*x^14 + 198197/326592000*x^13 - 15854113/1306368000*x^12 + 329951969/1828915200*x^11 - 742121123/365783040*x^10 + 318182501783/18289152000*x^9 - 260103473681/2286144000*x^8 + 7361464837/13063680*x^7 - 6801091211/3265920*x^6 + 711179678911/127008000*x^5 - 167040615887/15876000*x^4 + 2279113129/176400*x^3 - 40391903/4410*x^2 + 19448/7*x
17
8:
-1/14631321600*x^17 + 29/2926264320*x^16 - 2413/3657830400*x^15 + 13963/522547200*x^14 - 153841/209018880*x^13 + 15249989/1045094400*x^12 - 786305999/3657830400*x^11 + 8760225503/3657830400*x^10 - 297597678737/14631321600*x^9 + 275331981719/2090188800*x^8 - 168808112887/261273600*x^7 + 617900564479/261273600*x^6 - 23712241859/3763200*x^5 + 1192738437929/101606400*x^4 - 2018511721/141120*x^3 + 40610693/4032*x^2 - 12155/4*x
17
9:
1/14631321600*x^17 - 1/101606400*x^16 + 793/1219276800*x^15 - 253/9676800*x^14 + 35557/49766400*x^13 - 45319/3225600*x^12 + 750779977/3657830400*x^11 - 460758539/203212800*x^10 + 93117787187/4877107200*x^9 - 237291673/1935360*x^8 + 7420510091/12441600*x^7 - 873285587/403200*x^6 + 1047557035061/182891520*x^5 - 134599688021/12700800*x^4 + 16300730063/1270080*x^3 - 4531207/504*x^2 + 24310/9*x
17
10:
-1/18289152000*x^17 + 143/18289152000*x^16 - 4691/9144576000*x^15 + 191/9331200*x^14 - 725213/1306368000*x^13 + 14151499/1306368000*x^12 - 359001613/2286144000*x^11 + 1574128247/914457600*x^10 - 263099245433/18289152000*x^9 + 239587549657/2612736000*x^8 - 578622630139/1306368000*x^7 + 208723556891/130636800*x^6 - 1066662077597/254016000*x^5 + 30664759109/3969000*x^4 - 16423792051/1764000*x^3 + 40916999/6300*x^2 - 9724/5*x
17
11:
1/28740096000*x^17 - 71/14370048000*x^16 + 37/114960384*x^15 - 36643/2874009600*x^14 + 2466463/7185024000*x^13 - 95563217/14370048000*x^12 + 275083199/2874009600*x^11 - 38887717/37324800*x^10 + 22595084713/2612736000*x^9 - 17887500587/326592000*x^8 + 188918618243/718502400*x^7 - 169401713483/179625600*x^6 + 164040818297/66528000*x^5 - 112654459459/24948000*x^4 + 1502282653/277200*x^3 - 3729853/990*x^2 + 12376/11*x
17
12:
-1/57480192000*x^17 + 47/19160064000*x^16 - 19/119750400*x^15 + 1993/319334400*x^14 - 1598617/9580032000*x^13 + 10252799/3193344000*x^12 - 11993719/261273600*x^11 + 43241327/87091200*x^10 - 7134957121/1741824000*x^9 + 14976386687/580608000*x^8 - 117998298563/958003200*x^7 + 70193586719/159667200*x^6 - 4111022163019/3592512000*x^5 + 357094198049/171072000*x^4 - 49829919859/19958400*x^3 + 41121203/23760*x^2 - 1547/3*x
17
13:
1/149448499200*x^17 - 1/1067489280*x^16 + 281/4670265600*x^15 - 87821/37362124800*x^14 + 932989/14944849920*x^13 - 3430043/2874009600*x^12 + 553871/32659200*x^11 - 47646881/261273600*x^10 + 1563795019/1045094400*x^9 - 1224659407/130636800*x^8 + 64026063433/1437004800*x^7 - 14221892081/89812800*x^6 + 426143609293/1037836800*x^5 - 96839469833/129729600*x^4 + 1283237611/1441440*x^3 - 3169211/5148*x^2 + 2380/13*x
17
14:
-1/523069747200*x^17 + 139/523069747200*x^16 - 31/1828915200*x^15 + 43007/65383718400*x^14 - 7127/410572800*x^13 + 947987/2874009600*x^12 - 1065451/228614400*x^11 + 45584209/914457600*x^10 - 1488717127/3657830400*x^9 + 371382829/146313216*x^8 - 34528212673/2874009600*x^7 + 61127967839/1437004800*x^6 - 4840448243/44029440*x^5 + 90483119851/454053600*x^4 - 184001393/776160*x^3 + 41267063/252252*x^2 - 340/7*x
17
15:
1/2615348736000*x^17 - 23/435891456000*x^16 + 1457/435891456000*x^15 - 107/830269440*x^14 + 23/6804000*x^13 - 101977/1596672000*x^12 + 8208559/9144576000*x^11 - 5824703/609638400*x^10 + 473438827/6096384000*x^9 - 17503697/36288000*x^8 + 2723877539/1197504000*x^7 - 160212439/19958400*x^6 + 3381192445999/163459296000*x^5 - 254723226053/6810804000*x^4 + 4581289207/103194000*x^3 - 41325407/1351350*x^2 + 136/15*x
17
16:
-1/20922789888000*x^17 + 137/20922789888000*x^16 - 431/1046139494400*x^15 + 337/21349785600*x^14 - 47321/114960384000*x^13 + 889297/114960384000*x^12 - 158293/1463132160*x^11 + 8386453/7315660800*x^10 - 1357767871/146313216000*x^9 + 1200332081/20901888000*x^8 - 96966461/359251200*x^7 + 5459131639/5748019200*x^6 - 354672379021/145297152000*x^5 + 639824615137/145297152000*x^4 - 2105672501/403603200*x^3 + 20688229/5765760*x^2 - 17/16*x
17
17:
1/355687428096000*x^17 - 1/2615348736000*x^16 + 1/41845579776*x^15 - 17/18681062400*x^14 + 2713/114960384000*x^13 - 6341/14370048000*x^12 + 44941/7315660800*x^11 - 59279/914457600*x^10 + 76492463/146313216000*x^9 - 8424673/2612736000*x^8 + 86853967/5748019200*x^7 - 38101097/718502400*x^6 + 2195261857/16144128000*x^5 - 4446371981/18162144000*x^4 + 58433327/201801600*x^3 - 143327/720720*x^2 + 1/17*x
18
0:
1/6402373705728000*x^18 - 19/711374856192000*x^17 + 19/8966909952000*x^16 - 361/3487131648000*x^15 + 218861/62768369664000*x^14 - 28519/332107776000*x^13 + 526889/329204736000*x^12 - 18547097/804722688000*x^11 + 32547323/125411328000*x^10 - 224122879/97542144000*x^9 + 77238115183/4828336128000*x^8 - 185518261/2128896000*x^7 + 4325597501011/11769069312000*x^6 - 3084774343163/2615348736000*x^5 + 523771950307/186810624000*x^4 - 43007406851/9081072000*x^3 + 14911374857/2806876800*x^2 - 14274301/4084080*x + 1
18
1:
-1/355687428096000*x^18 + 1/2092278988800*x^17 - 197/5230697472000*x^16 + 191/104613949440*x^15 - 8279/135862272000*x^14 + 17069/11496038400*x^13 - 10994143/402361344000*x^12 + 1417543/3657830400*x^11 - 626792063/146313216000*x^10 + 542452567/14631321600*x^9 - 7209980513/28740096000*x^8 + 3787095691/2874009600*x^7 - 256595054171/48432384000*x^6 + 46299783613/2905943040*x^5 - 395976809/11466000*x^4 + 5116885451/100900800*x^3 - 30570663/680680*x^2 + 18*x
18
2:
1/41845579776000*x^18 - 13/3218890752000*x^17 + 3307/10461394944000*x^16 - 31817/2092278988800*x^15 + 1503653/2988969984000*x^14 - 2789489/229920768000*x^13 + 177530063/804722688000*x^12 - 45139013/14631321600*x^11 + 9813833791/292626432000*x^10 - 83244733879/292626432000*x^9 + 6748776343/3592512000*x^8 - 110083018643/11496038400*x^7 + 10775837950201/290594304000*x^6 - 2376114456413/22353408000*x^5 + 97035105411/448448000*x^4 - 117787176847/403603200*x^3 + 36696783/160160*x^2 - 153/2*x
18
3:
-1/7846046208000*x^18 + 1/46702656000*x^17 - 311/186810624000*x^16 + 533/6706022400*x^15 - 1087/416988000*x^14 + 298187/4790016000*x^13 - 337755629/301771008000*x^12 + 4036489/261273600*x^11 - 432209821/2612736000*x^10 + 4202399041/3048192000*x^9 - 32036087609/3592512000*x^8 + 5311679419/119750400*x^7 - 81816333371959/490377888000*x^6 + 5393368437811/11675664000*x^5 - 109711084919/121621500*x^4 + 10114193239/8731800*x^3 - 12912941/15015*x^2 + 272*x
18
4:
1/2092278988800*x^18 - 167/2092278988800*x^17 + 6449/1046139494400*x^16 - 13891/47551795200*x^15 + 202847/21349785600*x^14 - 2583919/11496038400*x^13 + 8044081/2011806720*x^12 - 199470851/3657830400*x^11 + 1685572139/2926264320*x^10 - 69160958681/14631321600*x^9 + 345371826193/11496038400*x^8 - 210502054999/1437004800*x^7 + 1304584574347/2421619200*x^6 - 1921012186313/1320883200*x^5 + 2229621554183/807206400*x^4 - 138976422337/40360320*x^3 + 39759843/16016*x^2 - 765*x
18
5:
-1/747242496000*x^18 + 83/373621248000*x^17 - 199/11675664000*x^16 + 21397/26687232000*x^15 - 9664121/373621248000*x^14 + 4357193/7185024000*x^13 - 38371139/3592512000*x^12 + 26886793/186624000*x^11 - 1122177613/746496000*x^10 + 31798092503/2612736000*x^9 - 547562196667/7185024000*x^8 + 1313410285001/3592512000*x^7 - 6855405167701/5189184000*x^6 + 9082068997633/2594592000*x^5 - 4895404253/750750*x^4 + 143677406107/18018000*x^3 - 8074491/1430*x^2 + 8568/5*x
18
6:
1/344881152000*x^18 - 1/2090188800*x^17 + 131/3592512000*x^16 - 3263/1916006400*x^15 + 3133297/57480192000*x^14 - 4855451/3832012800*x^13 + 1906248433/86220288000*x^12 - 22036957/74649600*x^11 + 4548523543/1492992000*x^10 - 3396565567/139345920*x^9 + 4331561838559/28740096000*x^8 - 6213364373/8709120*x^7 + 1957209074833/769824000*x^6 - 9543956662133/1437004800*x^5 + 3652269693967/299376000*x^4 - 146897160967/9979200*x^3 + 4531207/440*x^2 - 3094*x
18
7:
-1/201180672000*x^18 + 41/50295168000*x^17 - 887/14370048000*x^16 + 57587/20118067200*x^15 - 4573183/50295168000*x^14 + 4303471/2052864000*x^13 - 3647378083/100590336000*x^12 + 877249187/1828915200*x^11 - 12806383279/2612736000*x^10 + 354914219161/9144576000*x^9 - 5970118872733/25147584000*x^8 + 15971073191/14370048*x^7 - 607993725179/155232000*x^6 + 7068779573747/698544000*x^5 - 6372720769/346500*x^4 + 21319856221/970200*x^3 - 41072583/2695*x^2 + 31824/7*x
18
8:
1/146313216000*x^18 - 163/146313216000*x^17 + 6131/73156608000*x^16 - 5647/1463132160*x^15 + 1271873/10450944000*x^14 - 29095679/10450944000*x^13 + 873527653/18289152000*x^12 - 4582746697/7315660800*x^11 + 928333914953/146313216000*x^10 - 7284082089299/146313216000*x^9 + 3153220287019/10450944000*x^8 - 731289319289/522547200*x^7 + 2482767240773/508032000*x^6 - 12716887981403/1016064000*x^5 + 424492968923/18816000*x^4 - 37754585233/1411200*x^3 + 41291373/2240*x^2 - 21879/4*x
18
9:
-1/131681894400*x^18 + 1/812851200*x^17 - 1009/10973491200*x^16 + 641/152409600*x^15 - 412843/3135283200*x^14 + 520813/174182400*x^13 - 335166281/6584094720*x^12 + 100961543/152409600*x^11 - 58433095207/8778792960*x^10 + 126338621407/2438553600*x^9 - 244149825767/783820800*x^8 + 62422997681/43545600*x^7 - 40888795978993/8230118400*x^6 + 1925394642463/152409600*x^5 - 161612605313/7144200*x^4 + 16935099043/635040*x^3 - 41461543/2268*x^2 + 48620/9*x
18
10:
1/146313216000*x^18 - 23/20901888000*x^17 + 61/746496000*x^16 - 135809/36578304000*x^15 + 1206533/10450944000*x^14 - 27205333/10450944000*x^13 + 1609547663/36578304000*x^12 - 2970671329/5225472000*x^11 + 118540773479/20901888000*x^10 - 6412899265393/146313216000*x^9 + 683727644263/2612736000*x^8 - 3125610727853/2612736000*x^7 + 1395331094797/338688000*x^6 - 215943489589/20736000*x^5 + 37391694989/2016000*x^4 - 153542508319/7056000*x^3 + 41597679/2800*x^2 - 21879/5*x
18
11:
-1/201180672000*x^18 + 1/1257379200*x^17 - 5903/100590336000*x^16 + 53293/20118067200*x^15 - 293957/3592512000*x^14 + 752473/410572800*x^13 - 281413991/9144576000*x^12 + 7945851791/20118067200*x^11 - 71593608133/18289152000*x^10 + 54981152953/1828915200*x^9 - 640902601063/3592512000*x^8 + 41613693697/51321600*x^7 - 3880156724551/1397088000*x^6 + 975943986371/139708800*x^5 - 3337940909/269500*x^4 + 14042723297/970200*x^3 - 344703/35*x^2 + 31824/11*x
18
12:
1/344881152000*x^18 - 53/114960384000*x^17 + 1943/57480192000*x^16 - 83/54743040*x^15 + 243167/5225472000*x^14 - 19844501/19160064000*x^13 + 23283301/1347192000*x^12 - 16457663/74649600*x^11 + 3243119263/1492992000*x^10 - 57786129413/3483648000*x^9 + 5627969831669/57480192000*x^8 - 53023560301/119750400*x^7 + 16269712392107/10777536000*x^6 - 27165792364457/7185024000*x^5 + 727025214329/108864000*x^4 - 155246727997/19958400*x^3 + 13933961/2640*x^2 - 1547*x
18
13:
-1/747242496000*x^18 + 79/373621248000*x^17 - 1439/93405312000*x^16 + 25657/37362124800*x^15 - 7826501/373621248000*x^14 + 10821883/23351328000*x^13 - 55240711/7185024000*x^12 + 3640123/37324800*x^11 - 713481493/746496000*x^10 + 18972792799/2612736000*x^9 - 306508626019/7185024000*x^8 + 138001941509/718502400*x^7 - 161157007721/247104000*x^6 + 4222650362969/2594592000*x^5 - 3226739309/1126125*x^4 + 11992828039/3603600*x^3 - 3221571/1430*x^2 + 8568/13*x
18
14:
1/2092278988800*x^18 - 157/2092278988800*x^17 + 29/5337446400*x^16 - 125911/523069747200*x^15 + 7636403/1046139494400*x^14 - 1845989/11496038400*x^13 + 4264121/1609445376*x^12 - 122296681/3657830400*x^11 + 27261601/83607552*x^10 - 36081479011/14631321600*x^9 + 580434995243/40236134400*x^8 - 6640747891/102643200*x^7 + 1590329758361/7264857600*x^6 - 7911930599663/14529715200*x^5 + 9186968107/9609600*x^4 - 22353504241/20180160*x^3 + 41947743/56056*x^2 - 1530/7*x
18
15:
-1/7846046208000*x^18 + 1/50295168000*x^17 - 1871/1307674368000*x^16 + 2497/39626496000*x^15 - 177473/93405312000*x^14 + 28447/684288000*x^13 - 205936067/301771008000*x^12 + 78374869/9144576000*x^11 - 1521885367/18289152000*x^10 + 1910419997/3048192000*x^9 - 13121073557/3592512000*x^8 + 1396251001/85536000*x^7 - 26999710203379/490377888000*x^6 + 78059232463/571536000*x^5 - 203640964859/851350500*x^4 + 156968100811/567567000*x^3 - 4667343/25025*x^2 + 272/5*x
18
16:
1/41845579776000*x^18 - 31/8369115955200*x^17 + 5543/20922789888000*x^16 - 1867/160944537600*x^15 + 1039793/2988969984000*x^14 - 9949/1313832960*x^13 + 49778143/402361344000*x^12 - 22632823/14631321600*x^11 + 4376890951/292626432000*x^10 - 6568429249/58525286400*x^9 + 149862143539/229920768000*x^8 - 4769353201/1642291200*x^7 + 17522081943/1793792000*x^6 - 1404785487503/58118860800*x^5 + 681938065157/16144128000*x^4 - 378368087/7761600*x^3 + 21028569/640640*x^2 - 153/16*x
18
17:
-1/355687428096000*x^18 + 1/2309658624000*x^17 - 23/747242496000*x^16 + 701/523069747200*x^15 - 59749/1494484992000*x^14 + 49781/57480192000*x^13 - 5667619/402361344000*x^12 + 18331/104509440*x^11 - 35316569/20901888000*x^10 + 924323011/73156608000*x^9 - 2102355089/28740096000*x^8 + 84917281/261273600*x^7 - 158445349793/145297152000*x^6 + 27943099763/10378368000*x^5 - 28205587/6006000*x^4 + 545965723/100900800*x^3 - 2476599/680680*x^2 + 18/17*x
18
18:
1/6402373705728000*x^18 - 1/41845579776000*x^17 + 53/31384184832000*x^16 - 17/232475443200*x^15 + 19463/8966909952000*x^14 - 3587/76640256000*x^13 + 5490071/7242504192000*x^12 - 137581/14631321600*x^11 + 79243781/877879296000*x^10 - 7292813/10838016000*x^9 + 334947281/86220288000*x^8 - 13195009/766402560*x^7 + 1356664151597/23538138624000*x^6 - 371446039969/2615348736000*x^5 + 80847323107/326918592000*x^4 - 344499373/1210809600*x^3 + 42142223/220540320*x^2 - 1/18*x
19
0:
-1/121645100408832000*x^19 + 1/640237370572800*x^18 - 59/426824913715200*x^17 + 19/2510734786560*x^16 - 18017/62768369664000*x^15 + 10051/1255367393280*x^14 - 6406481/37661021798400*x^13 + 815081/289700167680*x^12 - 354467473/9656672256000*x^11 + 33399473/87787929600*x^10 - 6063698587/1931334451200*x^9 + 3975325483/193133445120*x^8 - 5013017410969/47076277248000*x^7 + 2022480780283/4707627724800*x^6 - 694142313941/523069747200*x^5 + 31938836201/10461394944*x^4 - 32262100943/6432426000*x^3 + 169704792667/30875644800*x^2 - 275295799/77597520*x + 1
19
1:
1/6402373705728000*x^19 - 1/33874993152000*x^18 + 163/62768369664000*x^17 - 211/1494484992000*x^16 + 333461/62768369664000*x^15 - 62687/426995712000*x^14 + 5586257/1810626048000*x^13 - 5790769/114960384000*x^12 + 568041581/877879296000*x^11 - 275136109/41803776000*x^10 + 256247462293/4828336128000*x^9 - 19428954073/57480192000*x^8 + 2479219294457/1471133664000*x^7 - 2420129609771/373621248000*x^6 + 24501306277999/1307674368000*x^5 - 50945862797/1297296000*x^4 + 1729792071433/30875644800*x^3 - 197698279/4084080*x^2 + 19*x
19
2:
-1/711374856192000*x^19 + 47/177843714048000*x^18 - 967/41845579776000*x^17 + 6527/5230697472000*x^16 - 74981/1609445376000*x^15 + 953423/747242496000*x^14 - 14236513/536481792000*x^13 + 21528371/50295168000*x^12 - 1586274043/292626432000*x^11 + 3966287881/73156608000*x^10 - 1379120763767/3218890752000*x^9 + 153061358911/57480192000*x^8 - 67390163486609/5230697472000*x^7 + 385017008149/8072064000*x^6 - 38222295237667/290594304000*x^5 + 1045345576103/4036032000*x^4 - 179264019481/527788800*x^3 + 709491117/2722720*x^2 - 171/2*x
19
3:
1/125536739328000*x^19 - 17/11412430848000*x^18 + 43/332107776000*x^17 - 72649/10461394944000*x^16 + 5383597/20922789888000*x^15 - 20881837/2988969984000*x^14 + 173671367/1207084032000*x^13 - 5539750873/2414168064000*x^12 + 1199142731/41803776000*x^11 - 82698300439/292626432000*x^10 + 3531914651759/1609445376000*x^9 - 69821458831/5225472000*x^8 + 247545775283627/3923023104000*x^7 - 1781031808455283/7846046208000*x^6 + 113006264470633/186810624000*x^5 - 31155416270059/27243216000*x^4 + 2595827563993/1816214400*x^3 - 249429959/240240*x^2 + 323*x
19
4:
-1/31384184832000*x^19 + 31/5230697472000*x^18 - 487/951035904000*x^17 + 142711/5230697472000*x^16 - 583183/581188608000*x^15 + 10094933/373621248000*x^14 - 665424467/1207084032000*x^13 + 1750310047/201180672000*x^12 - 7862548457/73156608000*x^11 + 38215051981/36578304000*x^10 - 2143316214559/268240896000*x^9 + 2748693712553/57480192000*x^8 - 39491420009819/178319232000*x^7 + 169853775525001/217945728000*x^6 - 441624734914711/217945728000*x^5 + 45142337976217/12108096000*x^4 - 2740746828763/605404800*x^3 + 255896419/80080*x^2 - 969*x
19
5:
1/10461394944000*x^19 - 37/2092278988800*x^18 + 227/149448499200*x^17 - 647/8047226880*x^16 + 15355723/5230697472000*x^15 - 11719781/149448499200*x^14 + 10635263/6706022400*x^13 - 39891917/1609445376*x^12 + 3165573881/10450944000*x^11 - 42569161507/14631321600*x^10 + 1767210023959/80472268800*x^9 - 74460013181/574801920*x^8 + 96527746726139/163459296000*x^7 - 9894455745439/4843238400*x^6 + 5413652230097/1037836800*x^5 - 7310713063/776160*x^4 + 2831609302633/252252000*x^3 - 155865777/20020*x^2 + 11628/5*x
19
6:
-1/4483454976000*x^19 + 23/560431872000*x^18 - 5237/1494484992000*x^17 + 68857/373621248000*x^16 - 4993207/747242496000*x^15 + 1504141/8491392000*x^14 - 612608267/172440576000*x^13 + 2371977137/43110144000*x^12 - 331347877/497664000*x^11 + 8266308161/1306368000*x^10 - 5428262508997/114960384000*x^9 + 7907982874117/28740096000*x^8 - 346985313735649/280215936000*x^7 + 1184394577743151/280215936000*x^6 - 994330355557843/93405312000*x^5 + 6709094455853/353808000*x^4 - 2893813833133/129729600*x^3 + 87454293/5720*x^2 - 4522*x
19
7:
1/2414168064000*x^19 - 61/804722688000*x^18 + 863/134120448000*x^17 - 67651/201180672000*x^16 + 4872377/402361344000*x^15 - 128217011/402361344000*x^14 + 478369349/75442752000*x^13 - 19591481477/201180672000*x^12 + 28480225387/24385536000*x^11 - 804359138143/73156608000*x^10 + 32685849098527/402361344000*x^9 - 47127212222059/100590336000*x^8 + 157383291769937/75442752000*x^7 - 118104486153103/16765056000*x^6 + 147154216971497/8382528000*x^5 - 1801743005659/58212000*x^4 + 419863398079/11642400*x^3 - 264210439/10780*x^2 + 50388/7*x
19
8:
-1/1609445376000*x^19 + 13/114960384000*x^18 - 15359/1609445376000*x^17 + 56977/114960384000*x^16 - 14267761/804722688000*x^15 + 26630633/57480192000*x^14 - 74382181/8128512000*x^13 + 8015397757/57480192000*x^12 - 242707059983/146313216000*x^11 + 161833938139/10450944000*x^10 - 182542643714947/1609445376000*x^9 + 10648138834163/16422912000*x^8 - 575687017995013/201180672000*x^7 + 5098192530037/532224000*x^6 - 264543491968499/11176704000*x^5 + 524618013019/12672000*x^4 - 67577334947/1411200*x^3 + 796788327/24640*x^2 - 37791/4*x
19
9:
1/1316818944000*x^19 - 181/1316818944000*x^18 + 2531/219469824000*x^17 - 65323/109734912000*x^16 + 4643677/219469824000*x^15 - 17218651/31352832000*x^14 + 443258861/41150592000*x^13 - 53648489983/329204736000*x^12 + 844627039331/438939648000*x^11 - 7825239229991/438939648000*x^10 + 28440099382073/219469824000*x^9 - 5762460647831/7838208000*x^8 + 33131222581433/10287648000*x^7 - 880858434293869/82301184000*x^6 + 120090701360423/4572288000*x^5 - 13044637460723/285768000*x^4 + 333376113857/6350400*x^3 - 800021557/22680*x^2 + 92378/9*x
19
10:
-1/1316818944000*x^19 + 1/7315660800*x^18 - 143/12541132800*x^17 + 107/182891520*x^16 - 4535491/219469824000*x^15 + 278497/522547200*x^14 - 1367480923/131681894400*x^13 + 2114243/13547520*x^12 - 114770598161/62705664000*x^11 + 24643135709/1463132160*x^10 - 10675588941413/87787929600*x^9 + 5116328879/7464960*x^8 - 491054105923487/164602368000*x^7 + 9011510339329/914457600*x^6 - 6282537230909/261273600*x^5 + 211207218007/5080320*x^4 - 3022133809141/63504000*x^3 + 267536047/8400*x^2 - 46189/5*x
19
11:
1/1609445376000*x^19 - 179/1609445376000*x^18 + 7423/804722688000*x^17 - 189311/402361344000*x^16 + 13293631/804722688000*x^15 - 48677287/114960384000*x^14 + 549859643/67060224000*x^13 - 49272391537/402361344000*x^12 + 2297241529753/1609445376000*x^11 - 1910090084057/146313216000*x^10 + 75400577665649/804722688000*x^9 - 15090107978987/28740096000*x^8 + 114316577340247/50295168000*x^7 - 9275824181131/1241856000*x^6 + 101366621541373/5588352000*x^5 - 1211789407363/38808000*x^4 + 276366909803/7761600*x^3 - 73156767/3080*x^2 + 75582/11*x
19
12:
-1/2414168064000*x^19 + 89/1207084032000*x^18 - 233/38320128000*x^17 + 124067/402361344000*x^16 - 4330687/402361344000*x^15 + 7882529/28740096000*x^14 - 6373672199/1207084032000*x^13 + 47321094781/603542016000*x^12 - 9497031203/10450944000*x^11 + 302346625109/36578304000*x^10 - 47487842805289/804722688000*x^9 + 18911819392313/57480192000*x^8 - 106940000506817/75442752000*x^7 + 699746447993437/150885504000*x^6 - 11512933042253/1026432000*x^5 + 161263073474581/8382528000*x^4 - 3055028577103/139708800*x^3 + 268829339/18480*x^2 - 4199*x
19
13:
1/4483454976000*x^19 - 59/1494484992000*x^18 + 2419/747242496000*x^17 - 60989/373621248000*x^16 + 1411259/249080832000*x^15 - 107284549/747242496000*x^14 + 1540592351/560431872000*x^13 - 1166864791/28740096000*x^12 + 698909411/1492992000*x^11 - 44279541389/10450944000*x^10 + 64090718507/2128896000*x^9 - 2401227769817/14370048000*x^8 + 50222768055721/70053984000*x^7 - 72746946806617/31135104000*x^6 + 87664764264347/15567552000*x^5 - 1040892890131/108108000*x^4 + 235982091661/21621600*x^3 - 20717443/2860*x^2 + 27132/13*x
19
14:
-1/10461394944000*x^19 + 1/59439744000*x^18 - 14351/10461394944000*x^17 + 179909/2615348736000*x^16 - 12421021/5230697472000*x^15 + 19567291/326918592000*x^14 - 152907529/134120448000*x^13 + 1685360483/100590336000*x^12 - 14065327931/73156608000*x^11 + 990049237/571536000*x^10 - 9862769094271/804722688000*x^9 + 1239221643899/18289152000*x^8 - 47342969775011/163459296000*x^7 + 22781487139127/24216192000*x^6 - 164217377171381/72648576000*x^5 + 3889135317103/1009008000*x^4 - 439817768059/100900800*x^3 + 809259357/280280*x^2 - 5814/7*x
19
15:
1/31384184832000*x^19 - 1/179338199040*x^18 + 43/95103590400*x^17 - 337/14944849920*x^16 + 311557/402361344000*x^15 - 2902001/149448499200*x^14 + 11107337/30177100800*x^13 - 18569017/3448811520*x^12 + 1500043463/24385536000*x^11 - 164809559/298598400*x^10 + 313044679543/80472268800*x^9 - 2463543517/114960384*x^8 + 8140415590423/89159616000*x^7 - 16570551866213/56043187200*x^6 + 46327293445687/65383718400*x^5 - 46910062669/38918880*x^4 + 237557634973/174636000*x^3 - 90040877/100100*x^2 + 1292/5*x
19
16:
-1/125536739328000*x^19 + 29/20922789888000*x^18 - 1559/13948526592000*x^17 + 116009/20922789888000*x^16 - 3963347/20922789888000*x^15 + 7065007/1494484992000*x^14 - 430675547/4828336128000*x^13 + 1045458233/804722688000*x^12 - 1441929299/97542144000*x^11 + 19333845719/146313216000*x^10 - 2987359524917/3218890752000*x^9 + 1171696725127/229920768000*x^8 - 339711799904303/15692092416000*x^7 + 60956895658069/871782912000*x^6 - 145729506485611/871782912000*x^5 + 13743828858943/48432384000*x^4 - 193537834213/605404800*x^3 + 135222977/640640*x^2 - 969/16*x
19
17:
1/711374856192000*x^19 - 173/711374856192000*x^18 + 991/50812489728000*x^17 - 10069/10461394944000*x^16 + 684623/20922789888000*x^15 - 220867/271724544000*x^14 + 341347/22353408000*x^13 - 178259111/804722688000*x^12 + 104974369/41803776000*x^11 - 6545749699/292626432000*x^10 + 252049451791/1609445376000*x^9 - 49285647601/57480192000*x^8 + 37114128847/10216206000*x^7 - 1133888347583/96864768000*x^6 + 82808307119/2965248000*x^5 - 4340540497/91728000*x^4 + 182587958009/3430627200*x^3 - 47776101/1361360*x^2 + 171/17*x
19
18:
-1/6402373705728000*x^19 + 43/1600593426432000*x^18 - 269/125536739328000*x^17 + 127/1207084032000*x^16 - 223451/62768369664000*x^15 + 197369/2241727488000*x^14 - 23861059/14485008384000*x^13 + 21551743/905313024000*x^12 - 236086121/877879296000*x^11 + 524087423/219469824000*x^10 - 160974126749/9656672256000*x^9 + 2242410529/24634368000*x^8 - 18112893431869/47076277248000*x^7 + 7109285459/5746615875*x^6 - 856028149363/290594304000*x^5 + 125316459211/25147584000*x^4 - 345619714877/61751289600*x^3 + 812954477/220540320*x^2 - 19/18*x
19
19:
1/121645100408832000*x^19 - 1/711374856192000*x^18 + 1/8966909952000*x^17 - 19/3487131648000*x^16 + 11519/62768369664000*x^15 - 1501/332107776000*x^14 + 27731/329204736000*x^13 - 976163/804722688000*x^12 + 1713017/125411328000*x^11 - 11795941/97542144000*x^10 + 4065163957/4828336128000*x^9 - 9764119/2128896000*x^8 + 227663026369/11769069312000*x^7 - 162356544377/2615348736000*x^6 + 27566944753/186810624000*x^5 - 2263547729/9081072000*x^4 + 784809203/2806876800*x^3 - 751279/4084080*x^2 + 1/19*x
20
0:
1/2432902008176640000*x^20 - 1/11585247657984000*x^19 + 31/3658499260416000*x^18 - 1/1935713894400*x^17 + 3931/179338199040000*x^16 - 587/853991424000*x^15 + 12437081/753220435968000*x^14 - 31849/102478970880*x^13 + 384794917/82771476480000*x^12 - 7321967/131383296000*x^11 + 2965638101/5518098432000*x^10 - 109542331/26276659200*x^9 + 12196364570297/470762772480000*x^8 - 573738838201/4483454976000*x^7 + 6670985204447/13450364928000*x^6 - 31591404263/21349785600*x^5 + 52460655692911/15878903040000*x^4 - 13334148911/2520460800*x^3 + 665690574539/117327450240*x^2 - 55835135/15519504*x + 1
20
1:
-1/121645100408832000*x^20 + 1/582033973248000*x^19 - 179/1067062284288000*x^18 + 29/2853107712000*x^17 - 26879/62768369664000*x^16 + 76001/5706215424000*x^15 - 14919343/47076277248000*x^14 + 3883823/658409472000*x^13 - 840892069/9656672256000*x^12 + 902036311/877879296000*x^11 - 46937467057/4828336128000*x^10 + 4041256811/54867456000*x^9 - 5231332699189/11769069312000*x^8 + 4525446601157/2139830784000*x^7 - 1133978824339/145297152000*x^6 + 647583200071/29719872000*x^5 - 273473923819/6175128960*x^4 + 1726815331/28068768*x^3 - 201578155/3879876*x^2 + 20*x
20
2:
1/12804747411456000*x^20 - 1/61561285632000*x^19 + 6733/4268249137152000*x^18 - 5963/62768369664000*x^17 + 45361/11412430848000*x^16 - 1924621/15692092416000*x^15 + 1089140887/376610217984000*x^14 - 385774663/7242504192000*x^13 + 15001776451/19313344512000*x^12 - 247867877/27433728000*x^11 + 1623151366349/19313344512000*x^10 - 3012820947863/4828336128000*x^9 + 345961836704629/94152554496000*x^8 - 30717197904091/1810626048000*x^7 + 28675867373177/475517952000*x^6 - 209927696558189/1307674368000*x^5 + 2524812122717/8233505280*x^4 - 483965626799/1235025792*x^3 + 240376915/816816*x^2 - 95*x
20
3:
-1/2134124568576000*x^20 + 23/237124952064000*x^19 - 769/82081714176000*x^18 + 5867/10461394944000*x^17 - 487621/20922789888000*x^16 + 382873/536481792000*x^15 - 16361473/980755776000*x^14 + 81611801/268240896000*x^13 - 42363649453/9656672256000*x^12 + 14739898987/292626432000*x^11 - 742866335297/1609445376000*x^10 + 225841427341/67060224000*x^9 - 19057573229869/980755776000*x^8 + 2828095574873/32288256000*x^7 - 91327826418263/301771008000*x^6 + 254652014806639/326918592000*x^5 - 26481829554443/18525386880*x^4 + 41386339823/23750496*x^3 - 253309835/204204*x^2 + 380*x
20
4:
1/502146957312000*x^20 - 103/251073478656000*x^19 + 733/18598035456000*x^18 - 21809/9299017728000*x^17 + 8102867/83691159552000*x^16 - 123151001/41845579776000*x^15 + 17130261791/251073478656000*x^14 - 11905174811/9656672256000*x^13 + 75504278929/4291854336000*x^12 - 12982281839/65028096000*x^11 + 23244571515317/12875563008000*x^10 - 83540342424641/6437781504000*x^9 + 4620778157850863/62768369664000*x^8 - 10216796381885189/31384184832000*x^7 + 1279566748471577/1162377216000*x^6 - 4822528390933063/1743565824000*x^5 + 2394154240249/484323840*x^4 - 567495135029/96864768*x^3 + 259776295/64064*x^2 - 4845/4*x
20
5:
-1/156920924160000*x^20 + 41/31384184832000*x^19 - 653/5230697472000*x^18 + 3863/523069747200*x^17 - 880249/2905943040000*x^16 + 15940151/1743565824000*x^15 - 103120949/490377888000*x^14 + 454705897/120708403200*x^13 - 214222786279/4023613440000*x^12 + 1749403069/2926264320*x^11 - 716646421081/134120448000*x^10 + 127135006457/3353011200*x^9 - 1040038143386153/4903778880000*x^8 + 1811594252745077/1961511552000*x^7 - 334729237973849/108972864000*x^6 + 41316979324163/5448643200*x^5 - 5594582690237/420420000*x^4 + 2929804742143/189189000*x^3 - 263656171/25025*x^2 + 15504/5*x
20
6:
1/62768369664000*x^20 - 17/5230697472000*x^19 + 19391/62768369664000*x^18 - 47521/2615348736000*x^17 + 704317/951035904000*x^16 - 6450793/290594304000*x^15 + 15905771951/31384184832000*x^14 - 226459103/25147584000*x^13 + 609140420681/4828336128000*x^12 - 51324143407/36578304000*x^11 + 19976964872357/1609445376000*x^10 - 1947183078839/22353408000*x^9 + 118065123386779/245188944000*x^8 - 2708033617485377/1307674368000*x^7 + 2424625692866959/356638464000*x^6 - 5414452011875513/326918592000*x^5 + 31256303905633/1089728640*x^4 - 598597400279/18162144*x^3 + 88747585/4004*x^2 - 6460*x
20
7:
-1/31384184832000*x^20 + 29/4483454976000*x^19 - 457/747242496000*x^18 + 1909/53374464000*x^17 - 32807/22643712000*x^16 + 511711/11860992000*x^15 - 3836732561/3923023104000*x^14 + 1486961981/86220288000*x^13 - 27551274241/114960384000*x^12 + 3945325999/1492992000*x^11 - 443829136609/19160064000*x^10 + 55090648277/342144000*x^9 - 432145737550411/490377888000*x^8 + 1051181720882201/280215936000*x^7 - 5749779560617/471744000*x^6 + 16339465980841/555984000*x^5 - 217909583449/4324320*x^4 + 1771962293/30888*x^3 - 268090315/7007*x^2 + 77520/7*x
20
8:
1/19313344512000*x^20 - 101/9656672256000*x^19 + 2111/2145927168000*x^18 - 61381/1072963584000*x^17 + 674077/292626432000*x^16 - 109697347/1609445376000*x^15 + 14820413159/9656672256000*x^14 - 129746143489/4828336128000*x^13 + 265125940879/715309056000*x^12 - 395545351867/97542144000*x^11 + 226997057727689/6437781504000*x^10 - 782395080007819/3218890752000*x^9 + 796120258091237/603542016000*x^8 - 6720428568127123/1207084032000*x^7 + 218707668598549/12192768000*x^6 - 2876791463426369/67060224000*x^5 + 1812865600451/24837120*x^4 - 307379806687/3725568*x^3 + 269475985/4928*x^2 - 62985/4*x
20
9:
-1/14485008384000*x^20 + 67/4828336128000*x^19 - 9403/7242504192000*x^18 + 30211/402361344000*x^17 - 7256597/2414168064000*x^16 + 71134699/804722688000*x^15 - 3580993799/1810626048000*x^14 + 41523302581/1207084032000*x^13 - 6825760316633/14485008384000*x^12 + 749023636867/146313216000*x^11 - 106692491681983/2414168064000*x^10 + 30422953574197/100590336000*x^9 - 737583258347987/452656512000*x^8 + 2060618015774383/301771008000*x^7 - 9889400655182497/452656512000*x^6 + 217544018881669/4191264000*x^5 - 11035786973521/125737920*x^4 + 68915283131/698544*x^3 - 811661185/12474*x^2 + 167960/9*x
20
10:
1/13168189440000*x^20 - 1/65840947200*x^19 + 1241/877879296000*x^18 - 3569/43893964800*x^17 + 7103491/2194698240000*x^16 - 1297991/13716864000*x^15 + 2771105803/1316818944000*x^14 - 2395003021/65840947200*x^13 + 2173423651127/4389396480000*x^12 - 586520611381/109734912000*x^11 + 40247351792213/877879296000*x^10 - 2736798064453/8778792960*x^9 + 2747355141562487/1646023680000*x^8 - 71519712372181/10287648000*x^7 + 4993063878883/225792000*x^6 - 47779490540489/914457600*x^5 + 55823938310891/635040000*x^4 - 3123262434907/31752000*x^3 + 271415923/4200*x^2 - 92378/5*x
20
11:
-1/14485008384000*x^20 + 199/14485008384000*x^19 - 3071/2414168064000*x^18 + 87847/1207084032000*x^17 - 6955357/2414168064000*x^16 + 202204543/2414168064000*x^15 - 1676641987/905313024000*x^14 + 115255548697/3621252096000*x^13 - 2079677617571/4828336128000*x^12 + 22318607173229/4828336128000*x^11 - 95170162303973/2414168064000*x^10 + 80438940696859/301771008000*x^9 - 80308794575599/56582064000*x^8 + 5324004852281491/905313024000*x^7 - 936190797843163/50295168000*x^6 + 550457526371933/12573792000*x^5 - 341568302617/4656960*x^4 + 57116932489/698544*x^3 - 24738305/462*x^2 + 167960/11*x
20
12:
1/19313344512000*x^20 - 1/97542144000*x^19 + 18239/19313344512000*x^18 - 15727/292626432000*x^17 + 6812027/3218890752000*x^16 - 2984381/48771072000*x^15 + 12994996559/9656672256000*x^14 - 373932043/16257024000*x^13 + 5979501790373/19313344512000*x^12 - 967138809319/292626432000*x^11 + 180520357853249/6437781504000*x^10 - 18401853448457/97542144000*x^9 + 2413501038220133/2414168064000*x^8 - 50276226952183/12192768000*x^7 + 15687330117079931/1207084032000*x^6 - 556829673738883/18289152000*x^5 + 17042815920589/335301120*x^4 - 57393564859/1016064*x^3 + 272709215/7392*x^2 - 20995/2*x
20
13:
-1/31384184832000*x^20 + 197/31384184832000*x^19 - 1003/1743565824000*x^18 + 28393/871782912000*x^17 - 606667/475517952000*x^16 + 191960089/5230697472000*x^15 - 1574930293/1961511552000*x^14 + 107131420889/7846046208000*x^13 - 49055069309/268240896000*x^12 + 47375619643/24385536000*x^11 - 6601198952479/402361344000*x^10 + 5526737384131/50295168000*x^9 - 568684951225757/980755776000*x^8 + 4672543965717233/1961511552000*x^7 - 24701037343349/3302208000*x^6 + 475795965366451/27243216000*x^5 - 879910730437/30270240*x^4 + 48762657023/1513512*x^3 - 21015895/1001*x^2 + 77520/13*x
20
14:
1/62768369664000*x^20 - 1/320246784000*x^19 + 851/2988969984000*x^18 - 107/6671808000*x^17 + 311387/498161664000*x^16 - 106103/5930496000*x^15 + 12224926751/31384184832000*x^14 - 284212387/43110144000*x^13 + 20208394501/229920768000*x^12 - 693933437/746496000*x^11 + 199696061419/25546752000*x^10 - 35683267321/684288000*x^9 + 1075415354487829/3923023104000*x^8 - 628933962108187/560431872000*x^7 + 218729515074143/62270208000*x^6 - 18185537174791/2223936000*x^5 + 26089169531/1921920*x^4 - 1854630353/123552*x^3 + 273632995/28028*x^2 - 19380/7*x
20
15:
-1/156920924160000*x^20 + 1/804722688000*x^19 - 1769/15692092416000*x^18 + 661/104613949440*x^17 - 6409241/26153487360000*x^16 + 4057219/581188608000*x^15 - 593500867/3923023104000*x^14 + 102566837/40236134400*x^13 - 408470540837/12070840320000*x^12 + 26076189947/73156608000*x^11 - 1201368202553/402361344000*x^10 + 22181594591/1117670400*x^9 - 254943342041389/2451889440000*x^8 + 4268463769337/10059033600*x^7 - 1298920510971971/980755776000*x^6 + 50267738709883/16345929600*x^5 - 173449967105447/34054020000*x^4 + 3190355609167/567567000*x^3 - 91334169/25025*x^2 + 5168/5*x
20
16:
1/502146957312000*x^20 - 97/251073478656000*x^19 + 449/12875563008000*x^18 - 162779/83691159552000*x^17 + 2094509/27897053184000*x^16 - 2284321/1072963584000*x^15 + 11533387991/251073478656000*x^14 - 7443130169/9656672256000*x^13 + 131220325507/12875563008000*x^12 - 62591724689/585252864000*x^11 + 425713023751/476872704000*x^10 - 12691824108353/2145927168000*x^9 + 969538914851329/31384184832000*x^8 - 3945730059965651/31384184832000*x^7 + 34996600503769/89413632000*x^6 - 1580989524586597/1743565824000*x^5 + 2903596039159/1937295360*x^4 - 12303207377/7451136*x^3 + 137162915/128128*x^2 - 4845/16*x
20
17:
-1/2134124568576000*x^20 + 193/2134124568576000*x^19 - 107/13173608448000*x^18 + 8909/19760412672000*x^17 - 32951/1902071808000*x^16 + 10233073/20922789888000*x^15 - 164908993/15692092416000*x^14 + 424028951/2414168064000*x^13 - 2482639477/1072963584000*x^12 + 786746717/32514048000*x^11 - 324027306227/1609445376000*x^10 + 267541132027/201180672000*x^9 - 27175578150871/3923023104000*x^8 + 220639325081381/7846046208000*x^7 - 3461296134211/39626496000*x^6 + 22006889280967/108972864000*x^5 - 228620816651/686125440*x^4 + 37721549347/102918816*x^3 - 16153595/68068*x^2 + 1140/17*x
20
18:
1/12804747411456000*x^20 - 1/66691392768000*x^19 + 17159/12804747411456000*x^18 - 1549/20922789888000*x^17 + 32321/11412430848000*x^16 - 416473/5230697472000*x^15 + 641773687/376610217984000*x^14 - 68504089/2414168064000*x^13 + 21583957513/57940033536000*x^12 - 47347723/12192768000*x^11 + 622171058989/19313344512000*x^10 - 341542288529/1609445376000*x^9 + 103817823850249/94152554496000*x^8 - 35041427926459/7846046208000*x^7 + 59248267718153/4279661568000*x^6 - 41779494660821/1307674368000*x^5 + 11700090481031/222304642560*x^4 - 7933357279/137225088*x^3 + 824594105/22054032*x^2 - 95/9*x
20
19:
-1/121645100408832000*x^20 + 191/121645100408832000*x^19 - 149/1067062284288000*x^18 + 241/31384184832000*x^17 - 1669/5706215424000*x^16 + 514069/62768369664000*x^15 - 2055217/11769069312000*x^14 + 20987107/7242504192000*x^13 - 366181429/9656672256000*x^12 + 345985849/877879296000*x^11 - 15743145547/4828336128000*x^10 + 12931037629/603542016000*x^9 - 326808210901/2942267328000*x^8 + 10567729954153/23538138624000*x^7 - 18348828859/13208832000*x^6 + 1046330784599/326918592000*x^5 - 32510829361/6175128960*x^4 + 1783376939/308756448*x^3 - 14478505/3879876*x^2 + 20/19*x
20
20:
1/2432902008176640000*x^20 - 1/12804747411456000*x^19 + 59/8536498274304000*x^18 - 19/50214695731200*x^17 + 18017/1255367393280000*x^16 - 10051/25107347865600*x^15 + 6406481/753220435968000*x^14 - 815081/5794003353600*x^13 + 354467473/193133445120000*x^12 - 33399473/1755758592000*x^11 + 6063698587/38626689024000*x^10 - 3975325483/3862668902400*x^9 + 5013017410969/941525544960000*x^8 - 2022480780283/94152554496000*x^7 + 694142313941/10461394944000*x^6 - 31938836201/209227898880*x^5 + 32262100943/128648520000*x^4 - 169704792667/617512896000*x^3 + 275295799/1551950400*x^2 - 1/20*x
Definition
For integers $0 \leq i \leq d$ the Lagrange basis polynomial for the nodes $0, 1, \dots, d$ is $\ell_{d,i}(x) = \prod_{j \neq i} \frac{x - j}{i - j}$, the product taken over $0 \leq j \leq d$ with $j \neq i$. Parameters are given as $d$ then $i$, the degree before the index.
Parameters
$d$
—   integer ($0 \leq d \leq 20$)
$i$
—   integer ($0 \leq i \leq d$)
Formulas
(1)
$\ell_{d,i}(x) = \prod_{\substack{0 \leq j \leq d \\ j \neq i}} \frac{x - j}{i - j}$.
(2)
$\ell_{d,i}(k) = 1$ if $k = i$ and $0$ for every other integer $0 \leq k \leq d$. This is the property that makes them a basis for interpolation.
(3)
$\sum_{i=0}^{d} \ell_{d,i}(x) = 1$, since the constant polynomial $1$ interpolates the value $1$ at every node.
(4)
The polynomial of degree at most $d$ through the points $(0, y_0), \dots, (d, y_d)$ is $\sum_{i=0}^{d} y_i\, \ell_{d,i}(x)$.
(5)
For arbitrary distinct nodes $x_0, \dots, x_d$ the same construction gives $\ell_i(x) = \prod_{j \neq i} \frac{x - x_j}{x_i - x_j}$; this table is the case $x_j = j$.
(6)
$\ell_{d,i}$ has degree exactly $d$, with leading coefficient $\frac{(-1)^{d-i}}{i!\,(d-i)!}$.
Comments
(7)
The coefficients are rational rather than integral: the denominators are the products $\prod_{j \neq i}(i-j) = (-1)^{d-i}\, i!\,(d-i)!$, which is why the table holds $\mathbb{Q}[x]$ and not $\mathbb{Z}[x]$.
(8)
Equally spaced nodes are the classical example of interpolation behaving badly as the degree grows -- Runge's phenomenon -- so these are useful for seeing that happen rather than as a way to interpolate at high degree.
(9)
$\ell_{d,i}$ is the only polynomial of degree at most $d$ that takes the value $1$ at $x = i$ and $0$ at every other node, which is what makes these a basis for interpolation.
(10)
A different basis of the same space: the Bernstein basis Bernstein_basis_polynomials also spans the polynomials of degree at most $d$. Interpolation is immediate in this basis and awkward in that one; the convex hull property is the other way round.
Programs
(P1)
Sage
R. = QQ[]
def lagrange_basis(d, i):
    return R(prod((x - j) / (i - j) for j in range(d + 1) if j != i))

lagrange_basis(21, 0)            # the next degree after this table
Links
Data properties
Entries are of type: rational polynomial
Table is complete: false