History of Laguerre polynomials

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when	who	what
2026-09-16 11:22	bmatschke interactive	tags: Sheffer sequence. a tag is a family of tables, and these are the members of one. numberdb-data#112 asked for it; the membership is decided by the generating function each table gives, not by its title.	current reviewed
2026-08-14 21:32	bmatschke migration	how well the digits are known: exact (type Q[])
2026-08-13 22:08	bmatschke migration	how well the digits are known: exact (type Q[])
2026-08-09 09:16	flattening migration	entries rewritten as records with named parameters
2026-08-09 08:35	data-repository import migration	the current state of the data repository
2021-09-30 20:47	bmatschke data-repository@09e03d5c	from the data repository, 09e03d5c
2021-09-30 20:08	bmatschke data-repository@01d73f7e	from the data repository, 01d73f7e

What changed between 2026-08-14 21:32 and 2026-09-16 11:22

from line 33 (5 lines, 1 more than before) @@ -33,4 +33,5 @@

 - polynomial - orthogonal polynomials+- Sheffer sequence Data properties:   type: Q[]

from line 43 (65 lines, 48 fewer than before) @@ -42,113 +43,65 @@

   number-header: $L_n(x)$ Numbers:-- params:-    n: '0'-  number: '1'-- params:-    n: '1'-  number: -x + 1-- params:-    n: '2'-  number: 1/2*x^2 - 2*x + 1-- params:-    n: '3'-  number: -1/6*x^3 + 3/2*x^2 - 3*x + 1-- params:-    n: '4'-  number: 1/24*x^4 - 2/3*x^3 + 3*x^2 - 4*x + 1-- params:-    n: '5'-  number: -1/120*x^5 + 5/24*x^4 - 5/3*x^3 + 5*x^2 - 5*x + 1-- params:-    n: '6'-  number: 1/720*x^6 - 1/20*x^5 + 5/8*x^4 - 10/3*x^3 + 15/2*x^2 - 6*x + 1-- params:-    n: '7'-  number: -1/5040*x^7 + 7/720*x^6 - 7/40*x^5 + 35/24*x^4 - 35/6*x^3 + 21/2*x^2 - 7*x+  '0': '1'+  '1': -x + 1+  '2': 1/2*x^2 - 2*x + 1+  '3': -1/6*x^3 + 3/2*x^2 - 3*x + 1+  '4': 1/24*x^4 - 2/3*x^3 + 3*x^2 - 4*x + 1+  '5': -1/120*x^5 + 5/24*x^4 - 5/3*x^3 + 5*x^2 - 5*x + 1+  '6': 1/720*x^6 - 1/20*x^5 + 5/8*x^4 - 10/3*x^3 + 15/2*x^2 - 6*x + 1+  '7': -1/5040*x^7 + 7/720*x^6 - 7/40*x^5 + 35/24*x^4 - 35/6*x^3 + 21/2*x^2 - 7*x     + 1-- params:-    n: '8'-  number: 1/40320*x^8 - 1/630*x^7 + 7/180*x^6 - 7/15*x^5 + 35/12*x^4 - 28/3*x^3 +-    14*x^2 - 8*x + 1-- params:-    n: '9'-  number: -1/362880*x^9 + 1/4480*x^8 - 1/140*x^7 + 7/60*x^6 - 21/20*x^5 + 21/4*x^4-    - 14*x^3 + 18*x^2 - 9*x + 1-- params:-    n: '10'-  number: 1/3628800*x^10 - 1/36288*x^9 + 1/896*x^8 - 1/42*x^7 + 7/24*x^6 - 21/10*x^5+  '8': 1/40320*x^8 - 1/630*x^7 + 7/180*x^6 - 7/15*x^5 + 35/12*x^4 - 28/3*x^3 + 14*x^2+    - 8*x + 1+  '9': -1/362880*x^9 + 1/4480*x^8 - 1/140*x^7 + 7/60*x^6 - 21/20*x^5 + 21/4*x^4 -+    14*x^3 + 18*x^2 - 9*x + 1+  '10': 1/3628800*x^10 - 1/36288*x^9 + 1/896*x^8 - 1/42*x^7 + 7/24*x^6 - 21/10*x^5     + 35/4*x^4 - 20*x^3 + 45/2*x^2 - 10*x + 1-- params:-    n: '11'-  number: -1/39916800*x^11 + 11/3628800*x^10 - 11/72576*x^9 + 11/2688*x^8 - 11/168*x^7+  '11': -1/39916800*x^11 + 11/3628800*x^10 - 11/72576*x^9 + 11/2688*x^8 - 11/168*x^7     + 77/120*x^6 - 77/20*x^5 + 55/4*x^4 - 55/2*x^3 + 55/2*x^2 - 11*x + 1-- params:-    n: '12'-  number: 1/479001600*x^12 - 1/3326400*x^11 + 11/604800*x^10 - 11/18144*x^9 + 11/896*x^8+  '12': 1/479001600*x^12 - 1/3326400*x^11 + 11/604800*x^10 - 11/18144*x^9 + 11/896*x^8     - 11/70*x^7 + 77/60*x^6 - 33/5*x^5 + 165/8*x^4 - 110/3*x^3 + 33*x^2 - 12*x + 1-- params:-    n: '13'-  number: -1/6227020800*x^13 + 13/479001600*x^12 - 13/6652800*x^11 + 143/1814400*x^10+  '13': -1/6227020800*x^13 + 13/479001600*x^12 - 13/6652800*x^11 + 143/1814400*x^10     - 143/72576*x^9 + 143/4480*x^8 - 143/420*x^7 + 143/60*x^6 - 429/40*x^5 + 715/24*x^4     - 143/3*x^3 + 39*x^2 - 13*x + 1-- params:-    n: '14'-  number: 1/87178291200*x^14 - 1/444787200*x^13 + 13/68428800*x^12 - 13/1425600*x^11+  '14': 1/87178291200*x^14 - 1/444787200*x^13 + 13/68428800*x^12 - 13/1425600*x^11     + 143/518400*x^10 - 143/25920*x^9 + 143/1920*x^8 - 143/210*x^7 + 1001/240*x^6     - 1001/60*x^5 + 1001/24*x^4 - 182/3*x^3 + 91/2*x^2 - 14*x + 1-- params:-    n: '15'-  number: -1/1307674368000*x^15 + 1/5811886080*x^14 - 1/59304960*x^13 + 13/13685760*x^12+  '15': -1/1307674368000*x^15 + 1/5811886080*x^14 - 1/59304960*x^13 + 13/13685760*x^12     - 13/380160*x^11 + 143/172800*x^10 - 143/10368*x^9 + 143/896*x^8 - 143/112*x^7     + 1001/144*x^6 - 1001/40*x^5 + 455/8*x^4 - 455/6*x^3 + 105/2*x^2 - 15*x + 1-- params:-    n: '16'-  number: 1/20922789888000*x^16 - 1/81729648000*x^15 + 1/726485760*x^14 - 1/11119680*x^13+  '16': 1/20922789888000*x^16 - 1/81729648000*x^15 + 1/726485760*x^14 - 1/11119680*x^13     + 13/3421440*x^12 - 13/118800*x^11 + 143/64800*x^10 - 143/4536*x^9 + 143/448*x^8     - 143/63*x^7 + 1001/90*x^6 - 182/5*x^5 + 455/6*x^4 - 280/3*x^3 + 60*x^2 - 16*x     + 1-- params:-    n: '17'-  number: -1/355687428096000*x^17 + 17/20922789888000*x^16 - 17/163459296000*x^15-    + 17/2179457280*x^14 - 17/44478720*x^13 + 221/17107200*x^12 - 221/712800*x^11-    + 2431/453600*x^10 - 2431/36288*x^9 + 2431/4032*x^8 - 2431/630*x^7 + 1547/90*x^6+  '17': -1/355687428096000*x^17 + 17/20922789888000*x^16 - 17/163459296000*x^15 ++    17/2179457280*x^14 - 17/44478720*x^13 + 221/17107200*x^12 - 221/712800*x^11 ++    2431/453600*x^10 - 2431/36288*x^9 + 2431/4032*x^8 - 2431/630*x^7 + 1547/90*x^6     - 1547/30*x^5 + 595/6*x^4 - 340/3*x^3 + 68*x^2 - 17*x + 1-- params:-    n: '18'-  number: 1/6402373705728000*x^18 - 1/19760412672000*x^17 + 17/2324754432000*x^16-    - 17/27243216000*x^15 + 17/484323840*x^14 - 17/12355200*x^13 + 221/5702400*x^12+  '18': 1/6402373705728000*x^18 - 1/19760412672000*x^17 + 17/2324754432000*x^16 -+    17/27243216000*x^15 + 17/484323840*x^14 - 17/12355200*x^13 + 221/5702400*x^12     - 221/277200*x^11 + 2431/201600*x^10 - 2431/18144*x^9 + 2431/2240*x^8 - 221/35*x^7     + 1547/60*x^6 - 357/5*x^5 + 255/2*x^4 - 136*x^3 + 153/2*x^2 - 18*x + 1-- params:-    n: '19'-  number: -1/121645100408832000*x^19 + 19/6402373705728000*x^18 - 19/39520825344000*x^17+  '19': -1/121645100408832000*x^19 + 19/6402373705728000*x^18 - 19/39520825344000*x^17     + 323/6974263296000*x^16 - 323/108972864000*x^15 + 323/2421619200*x^14 - 323/74131200*x^13     + 4199/39916800*x^12 - 4199/2217600*x^11 + 46189/1814400*x^10 - 46189/181440*x^9     + 4199/2240*x^8 - 4199/420*x^7 + 2261/60*x^6 - 969/10*x^5 + 323/2*x^4 - 323/2*x^3     + 171/2*x^2 - 19*x + 1-- params:-    n: '20'-  number: 1/2432902008176640000*x^20 - 1/6082255020441600*x^19 + 19/640237370572800*x^18+  '20': 1/2432902008176640000*x^20 - 1/6082255020441600*x^19 + 19/640237370572800*x^18     - 19/5928123801600*x^17 + 323/1394852659200*x^16 - 323/27243216000*x^15 + 323/726485760*x^14     - 323/25945920*x^13 + 4199/15966720*x^12 - 4199/997920*x^11 + 46189/907200*x^10     - 4199/9072*x^9 + 4199/1344*x^8 - 323/21*x^7 + 323/6*x^6 - 646/5*x^5 + 1615/8*x^4     - 190*x^3 + 95*x^2 - 20*x + 1-- params:-    n: '21'-  number: -1/51090942171709440000*x^21 + 1/115852476579840000*x^20 - 1/579262382899200*x^19+  '21': -1/51090942171709440000*x^21 + 1/115852476579840000*x^20 - 1/579262382899200*x^19     + 19/91462481510400*x^18 - 19/1129166438400*x^17 + 323/332107776000*x^16 - 323/7783776000*x^15     + 323/242161920*x^14 - 323/9884160*x^13 + 4199/6842880*x^12 - 4199/475200*x^11     + 4199/43200*x^10 - 4199/5184*x^9 + 323/64*x^8 - 323/14*x^7 + 2261/30*x^6 - 6783/40*x^5     + 1995/8*x^4 - 665/3*x^3 + 105*x^2 - 21*x + 1-- params:-    n: '22'-  number: 1/1124000727777607680000*x^22 - 1/2322315553259520000*x^21 + 1/10532043325440000*x^20+  '22': 1/1124000727777607680000*x^22 - 1/2322315553259520000*x^21 + 1/10532043325440000*x^20     - 1/78990324940800*x^19 + 19/16629542092800*x^18 - 19/256628736000*x^17 + 323/90574848000*x^16     - 323/2476656000*x^15 + 323/88058880*x^14 - 323/4043520*x^13 + 4199/3110400*x^12     - 4199/237600*x^11 + 46189/259200*x^10 - 3553/2592*x^9 + 3553/448*x^8 - 3553/105*x^7     + 24871/240*x^6 - 4389/20*x^5 + 7315/24*x^4 - 770/3*x^3 + 231/2*x^2 - 22*x + 1-- params:-    n: '23'-  number: -1/25852016738884976640000*x^23 + 23/1124000727777607680000*x^22 - 23/4644631106519040000*x^21+  '23': -1/25852016738884976640000*x^23 + 23/1124000727777607680000*x^22 - 23/4644631106519040000*x^21     + 23/31596129976320000*x^20 - 23/315961299763200*x^19 + 437/83147710464000*x^18     - 437/1539772416000*x^17 + 7429/634023936000*x^16 - 7429/19813248000*x^15 + 7429/792529920*x^14

from line 109 (5 lines, 2 fewer than before) @@ -156,7 +109,5 @@

     - 81719/36288*x^9 + 81719/6720*x^8 - 81719/1680*x^7 + 33649/240*x^6 - 33649/120*x^5     + 8855/24*x^4 - 1771/6*x^3 + 253/2*x^2 - 23*x + 1-- params:-    n: '24'-  number: 1/620448401733239439360000*x^24 - 1/1077167364120207360000*x^23 + 23/93666727314800640000*x^22+  '24': 1/620448401733239439360000*x^24 - 1/1077167364120207360000*x^23 + 23/93666727314800640000*x^22     - 23/580578888314880000*x^21 + 23/5266021662720000*x^20 - 23/65825270784000*x^19     + 437/20786927616000*x^18 - 437/449100288000*x^17 + 7429/211341312000*x^16 - 7429/7429968000*x^15

from line 115 (5 lines, 2 fewer than before) @@ -164,7 +115,5 @@

     + 81719/151200*x^10 - 81719/22680*x^9 + 81719/4480*x^8 - 4807/70*x^7 + 33649/180*x^6     - 1771/5*x^5 + 1771/4*x^4 - 1012/3*x^3 + 138*x^2 - 24*x + 1-- params:-    n: '25'-  number: -1/15511210043330985984000000*x^25 + 1/24817936069329577574400*x^24 - 1/86173389129616588800*x^23+  '25': -1/15511210043330985984000000*x^25 + 1/24817936069329577574400*x^24 - 1/86173389129616588800*x^23     + 23/11240007277776076800*x^22 - 23/92892622130380800*x^21 + 23/1053204332544000*x^20     - 23/15798064988160*x^19 + 437/5820339732480*x^18 - 437/143712092160*x^17 + 7429/76082872320*x^16

from line 121 (5 lines, 2 fewer than before) @@ -172,7 +121,5 @@

     - 7429/66528*x^11 + 81719/90720*x^10 - 408595/72576*x^9 + 24035/896*x^8 - 24035/252*x^7     + 8855/36*x^6 - 1771/4*x^5 + 6325/12*x^4 - 1150/3*x^3 + 150*x^2 - 25*x + 1-- params:-    n: '26'-  number: 1/403291461126605635584000000*x^26 - 1/596585001666576384000000*x^25 + 1/1909072005333044428800*x^24+  '26': 1/403291461126605635584000000*x^26 - 1/596585001666576384000000*x^25 + 1/1909072005333044428800*x^24     - 1/9943083361109606400*x^23 + 23/1729231888888627200*x^22 - 23/17863965794304000*x^21     + 23/243047153664000*x^20 - 23/4253325189120*x^19 + 437/1790873763840*x^18 - 437/49746493440*x^17

from line 128 (5 lines, 2 fewer than before) @@ -181,7 +128,5 @@

     + 312455/8064*x^8 - 16445/126*x^7 + 23023/72*x^6 - 3289/6*x^5 + 7475/12*x^4 -     1300/3*x^3 + 325/2*x^2 - 26*x + 1-- params:-    n: '27'-  number: -1/10888869450418352160768000000*x^27 + 1/14936720782466875392000000*x^26+  '27': -1/10888869450418352160768000000*x^27 + 1/14936720782466875392000000*x^26     - 1/44191481604931584000000*x^25 + 1/212119111703671603200*x^24 - 1/1473049386831052800*x^23     + 23/320228127571968000*x^22 - 23/3969770176512000*x^21 + 23/63012225024000*x^20

from line 135 (5 lines, 2 fewer than before) @@ -190,7 +135,5 @@

     - 96577/295680*x^11 + 62491/26880*x^10 - 312455/24192*x^9 + 49335/896*x^8 - 9867/56*x^7     + 3289/8*x^6 - 2691/4*x^5 + 2925/4*x^4 - 975/2*x^3 + 351/2*x^2 - 27*x + 1-- params:-    n: '28'-  number: 1/304888344611713860501504000000*x^28 - 1/388888194657798291456000000*x^27+  '28': 1/304888344611713860501504000000*x^28 - 1/388888194657798291456000000*x^27     + 1/1066908627319062528000000*x^26 - 1/4734801600528384000000*x^25 + 1/30302730243381657600*x^24     - 1/263044533362688000*x^23 + 23/68620313051136000*x^22 - 23/992442544128000*x^21

from line 143 (5 lines, 2 fewer than before) @@ -200,7 +143,5 @@

     - 3289/14*x^7 + 2093/4*x^6 - 819*x^5 + 6825/8*x^4 - 546*x^3 + 189*x^2 - 28*x +     1-- params:-    n: '29'-  number: -1/8841761993739701954543616000000*x^29 + 29/304888344611713860501504000000*x^28+  '29': -1/8841761993739701954543616000000*x^29 + 29/304888344611713860501504000000*x^28     - 29/777776389315596582912000000*x^27 + 29/3200725881957187584000000*x^26 - 29/18939206402113536000000*x^25     + 29/151513651216908288000*x^24 - 29/1578267200176128000*x^23 + 667/480342191357952000*x^22

from line 151 (5 lines, 2 fewer than before) @@ -210,7 +151,5 @@

     - 164749/190080*x^11 + 95381/17280*x^10 - 95381/3456*x^9 + 95381/896*x^8 - 8671/28*x^7     + 2639/4*x^6 - 7917/8*x^5 + 7917/8*x^4 - 609*x^3 + 203*x^2 - 29*x + 1-- params:-    n: '30'-  number: 1/265252859812191058636308480000000*x^30 - 1/294725399791323398484787200000*x^29+  '30': 1/265252859812191058636308480000000*x^30 - 1/294725399791323398484787200000*x^29     + 29/20325889640780924033433600000*x^28 - 29/77777638931559658291200000*x^27 +     29/426763450927625011200000*x^26 - 29/3156534400352256000000*x^25 + 29/30302730243381657600*x^24

from line 160 (5 lines, 2 fewer than before) @@ -221,7 +160,5 @@

     476905/12096*x^9 + 130065/896*x^8 - 5655/14*x^7 + 13195/16*x^6 - 23751/20*x^5     + 9135/8*x^4 - 2030/3*x^3 + 435/2*x^2 - 30*x + 1-- params:-    n: '31'-  number: -1/8222838654177922817725562880000000*x^31 + 31/265252859812191058636308480000000*x^30+  '31': -1/8222838654177922817725562880000000*x^31 + 31/265252859812191058636308480000000*x^30     - 31/589450799582646796969574400000*x^29 + 899/60977668922342772100300800000*x^28     - 899/311110555726238633164800000*x^27 + 899/2133817254638125056000000*x^26 -

from line 170 (5 lines, 2 fewer than before) @@ -233,7 +170,5 @@

     - 1344005/24192*x^9 + 175305/896*x^8 - 58435/112*x^7 + 81809/80*x^6 - 56637/40*x^5     + 31465/24*x^4 - 4495/6*x^3 + 465/2*x^2 - 31*x + 1-- params:-    n: '32'-  number: 1/263130836933693530167218012160000000*x^32 - 1/256963707943060088053923840000000*x^31+  '32': 1/263130836933693530167218012160000000*x^32 - 1/256963707943060088053923840000000*x^31     + 31/16578303738261941164769280000000*x^30 - 31/55261012460873137215897600000*x^29     + 899/7622208615292846512537600000*x^28 - 899/48611024332224786432000000*x^27

from line 180 (5 lines, 2 fewer than before) @@ -245,7 +180,5 @@

     + 268801/15120*x^10 - 58435/756*x^9 + 58435/224*x^8 - 23374/35*x^7 + 6293/5*x^6     - 25172/15*x^5 + 4495/3*x^4 - 2480/3*x^3 + 248*x^2 - 32*x + 1-- params:-    n: '33'-  number: -1/8683317618811886495518194401280000000*x^33 + 1/7973661725263440308097515520000000*x^32+  '33': -1/8683317618811886495518194401280000000*x^33 + 1/7973661725263440308097515520000000*x^32     - 1/15573558057155156851752960000000*x^31 + 31/1507118521660176469524480000000*x^30     - 31/6698304540711895420108800000*x^29 + 899/1154880093226188865536000000*x^28

from line 190 (5 lines, 2 fewer than before) @@ -257,7 +190,5 @@

     - 268801/55440*x^11 + 128557/5040*x^10 - 642785/6048*x^9 + 385671/1120*x^8 - 29667/35*x^7     + 69223/45*x^6 - 9889/5*x^5 + 1705*x^4 - 2728/3*x^3 + 264*x^2 - 33*x + 1-- params:-    n: '34'-  number: 1/295232799039604140847618609643520000000*x^34 - 1/255391694670937838103476305920000000*x^33+  '34': 1/295232799039604140847618609643520000000*x^34 - 1/255391694670937838103476305920000000*x^33     + 1/469038925015496488711618560000000*x^32 - 1/1374137475631337369272320000000*x^31     + 31/177308061371785467002880000000*x^30 - 31/985044785398808150016000000*x^29

from line 201 (5 lines, 2 fewer than before) @@ -270,7 +201,5 @@

     + 2185469/60480*x^10 - 2185469/15120*x^9 + 504339/1120*x^8 - 336226/315*x^7 +     168113/90*x^6 - 11594/5*x^5 + 5797/3*x^4 - 2992/3*x^3 + 561/2*x^2 - 34*x + 1-- params:-    n: '35'-  number: -1/10333147966386144929666651337523200000000*x^35 + 1/8435222829702975452789103132672000000*x^34+  '35': -1/10333147966386144929666651337523200000000*x^35 + 1/8435222829702975452789103132672000000*x^34     - 1/14593811124053590748770074624000000*x^33 + 1/40203336429899699032424448000000*x^32     - 1/157044282929295699345408000000*x^31 + 31/25329723053112209571840000000*x^30

from line 212 (5 lines, 2 fewer than before) @@ -283,7 +212,5 @@

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from line 224 (5 lines, 2 fewer than before) @@ -297,7 +224,5 @@

     168113/224*x^8 - 11594/7*x^7 + 40579/15*x^6 - 15708/5*x^5 + 19635/8*x^4 - 1190*x^3     + 315*x^2 - 36*x + 1-- params:-    n: '37'-  number: -1/13763753091226345046315979581580902400000000*x^37 + 37/371993326789901217467999448150835200000000*x^36+  '37': -1/13763753091226345046315979581580902400000000*x^37 + 37/371993326789901217467999448150835200000000*x^36     - 37/574063775910341384981480629862400000000*x^35 + 37/1405870471617162575464850522112000000*x^34     - 37/4864603708017863582923358208000000*x^33 + 37/22335186905499832795791360000000*x^32

from line 237 (5 lines, 2 fewer than before) @@ -312,7 +237,5 @@

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from line 251 (5 lines, 2 fewer than before) @@ -328,7 +251,5 @@

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from line 265 (5 lines, 2 fewer than before) @@ -344,7 +265,5 @@

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from line 279 (5 lines, 2 fewer than before) @@ -360,7 +279,5 @@

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from line 295 (5 lines, 2 fewer than before) @@ -378,7 +295,5 @@

     + 374699/60*x^6 - 374699/60*x^5 + 50635/12*x^4 - 5330/3*x^3 + 410*x^2 - 41*x +     1-- params:-    n: '42'-  number: 1/1405006117752879898543142606244511569936384000000000*x^42 - 1/796488728884852550194525286986684563456000000000*x^41+  '42': 1/1405006117752879898543142606244511569936384000000000*x^42 - 1/796488728884852550194525286986684563456000000000*x^41     + 41/38853108726090368302171965218862661632000000000*x^40 - 41/72849578861419440566572434785367490560000000*x^39     + 41/191583376361392348630039276227133440000000*x^38 - 41/663377341971580154536147078348800000000*x^37

from line 311 (5 lines, 2 fewer than before) @@ -396,7 +311,5 @@

     - 374699/70*x^7 + 2622893/360*x^6 - 70889/10*x^5 + 18655/4*x^4 - 5740/3*x^3 +     861/2*x^2 - 42*x + 1-- params:-    n: '43'-  number: -1/60415263063373835637355132068513997507264512000000000*x^43 + 43/1405006117752879898543142606244511569936384000000000*x^42+  '43': -1/60415263063373835637355132068513997507264512000000000*x^43 + 43/1405006117752879898543142606244511569936384000000000*x^42     - 43/1592977457769705100389050573973369126912000000000*x^41 + 1763/116559326178271104906515895656587984896000000000*x^40     - 1763/291398315445677762266289739141469962240000000*x^39 + 1763/957916881806961743150196381135667200000000*x^38

from line 328 (5 lines, 2 fewer than before) @@ -415,7 +328,5 @@

     - 16112057/2520*x^7 + 3048227/360*x^6 - 160433/20*x^5 + 61705/12*x^4 - 12341/6*x^3     + 903/2*x^2 - 43*x + 1-- params:-    n: '44'-  number: 1/2658271574788448768043625811014615890319638528000000000*x^44 - 1/1373074160531223537212616637920772670619648000000000*x^43+  '44': 1/2658271574788448768043625811014615890319638528000000000*x^44 - 1/1373074160531223537212616637920772670619648000000000*x^43     + 43/63863914443312722661051936647477798633472000000000*x^42 - 43/108612099393388984117435266407275167744000000000*x^41     + 1763/10596302379842827718774172332417089536000000000*x^40 - 1763/33113444937008836621169288538803404800000000*x^39

from line 345 (5 lines, 2 fewer than before) @@ -434,7 +345,5 @@

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from line 362 (5 lines, 2 fewer than before) @@ -453,7 +362,5 @@

     - 177232627/72576*x^9 + 4790071/896*x^8 - 252109/28*x^7 + 135751/12*x^6 - 407253/40*x^5     + 49665/8*x^4 - 2365*x^3 + 495*x^2 - 45*x + 1-- params:-    n: '46'-  number: 1/5502622159812088949850305428800254892961651752960000000000*x^46 - 1/2600483062293047707868764380340385110095298560000000000*x^45+  '46': 1/5502622159812088949850305428800254892961651752960000000000*x^46 - 1/2600483062293047707868764380340385110095298560000000000*x^45     + 1/2568378333128936007771619141076923565526220800000000*x^44 - 1/3979925102989053731051062718610935277158400000000*x^43     + 43/370225590975725928469866299405668397875200000000*x^42 - 43/1049392264670424967318215134369808384000000000*x^41

from line 380 (5 lines, 2 fewer than before) @@ -473,7 +380,5 @@

     110171633/36288*x^9 + 5798507/896*x^8 - 446039/42*x^7 + 3122273/240*x^6 - 228459/20*x^5     + 54395/8*x^4 - 2530*x^3 + 1035/2*x^2 - 46*x + 1-- params:-    n: '47'-  number: -1/258623241511168180642964355153611979969197632389120000000000*x^47 + 47/5502622159812088949850305428800254892961651752960000000000*x^46+  '47': -1/258623241511168180642964355153611979969197632389120000000000*x^47 + 47/5502622159812088949850305428800254892961651752960000000000*x^46     - 47/5200966124586095415737528760680770220190597120000000000*x^45 + 47/7705134999386808023314857423230770696578662400000000*x^44     - 47/15919700411956214924204250874443741108633600000000*x^43 + 2021/1851127954878629642349331497028341989376000000000*x^42

from line 399 (25 lines, 5 fewer than before) @@ -494,30 +399,25 @@

     - 272529829/72576*x^9 + 20963833/2688*x^8 - 20963833/1680*x^7 + 3579191/240*x^6     - 511313/40*x^5 + 59455/8*x^4 - 5405/2*x^3 + 1081/2*x^2 - 47*x + 1-- params:-    n: '48'-  number: 1/12413915592536072670862289047373375038521486354677760000000000*x^48 --    1/5387984198149337096728424065700249582691617341440000000000*x^47 + 47/229275923325503706243762726200010620540068823040000000000*x^46-    - 47/325060382786630963483595547542548138761912320000000000*x^45 + 47/642094583282234001942904785269230891381555200000000*x^44-    - 47/1658302126245439054604609466087889698816000000000*x^43 + 2021/231390994359828705293666437128542748672000000000*x^42-    - 2021/918218231586621846403438242573582336000000000*x^41 + 82861/179164532992511579786036730258259968000000000*x^40-    - 82861/1007800498082877636296456607702712320000000*x^39 + 82861/6625907285226019962501358367539200000000*x^38-    - 82861/50474362976098490019054669004800000000*x^37 + 3065857/16370063667923834600774487244800000000*x^36-    - 3065857/164205885557877970532460134400000000*x^35 + 3065857/1876638692090033948942401536000000*x^34-    - 3065857/24350848080753035669667840000000*x^33 + 3065857/357771872628143774760960000000*x^32-    - 3065857/5939572104178168135680000000*x^31 + 95041567/3448783802426033111040000000*x^30-    - 95041567/72807658051216254566400000*x^29 + 2756205443/50212177966356037632000000*x^28-    - 2756205443/1344969052670251008000000*x^27 + 2756205443/40588915169746944000000*x^26-    - 2756205443/1380983800154112000000*x^25 + 2756205443/53029777925917900800*x^24-    - 2756205443/2301639666923520000*x^23 + 63392725189/2601853536522240000*x^22 --    63392725189/145144722078720000*x^21 + 63392725189/9215537909760000*x^20 - 2185956041/23038844774400*x^19-    + 41533164779/36377123328000*x^18 - 1339779509/112275072000*x^17 + 22776251653/211341312000*x^16-    - 22776251653/27243216000*x^15 + 1339779509/242161920*x^14 - 1339779509/43243200*x^13-    + 17417133617/119750400*x^12 - 470733341/831600*x^11 + 272529829/151200*x^10 --    20963833/4536*x^9 + 20963833/2240*x^8 - 511313/35*x^7 + 511313/30*x^6 - 71346/5*x^5-    + 16215/2*x^4 - 8648/3*x^3 + 564*x^2 - 48*x + 1-- params:-    n: '49'-  number: -1/608281864034267560872252163321295376887552831379210240000000000*x^49-    + 1/253345216174205564711475286681089286500438497034240000000000*x^48 - 1/219917722373442330478711186355112227864963973120000000000*x^47+  '48': 1/12413915592536072670862289047373375038521486354677760000000000*x^48 - 1/5387984198149337096728424065700249582691617341440000000000*x^47+    + 47/229275923325503706243762726200010620540068823040000000000*x^46 - 47/325060382786630963483595547542548138761912320000000000*x^45+    + 47/642094583282234001942904785269230891381555200000000*x^44 - 47/1658302126245439054604609466087889698816000000000*x^43+    + 2021/231390994359828705293666437128542748672000000000*x^42 - 2021/918218231586621846403438242573582336000000000*x^41+    + 82861/179164532992511579786036730258259968000000000*x^40 - 82861/1007800498082877636296456607702712320000000*x^39+    + 82861/6625907285226019962501358367539200000000*x^38 - 82861/50474362976098490019054669004800000000*x^37+    + 3065857/16370063667923834600774487244800000000*x^36 - 3065857/164205885557877970532460134400000000*x^35+    + 3065857/1876638692090033948942401536000000*x^34 - 3065857/24350848080753035669667840000000*x^33+    + 3065857/357771872628143774760960000000*x^32 - 3065857/5939572104178168135680000000*x^31+    + 95041567/3448783802426033111040000000*x^30 - 95041567/72807658051216254566400000*x^29+    + 2756205443/50212177966356037632000000*x^28 - 2756205443/1344969052670251008000000*x^27+    + 2756205443/40588915169746944000000*x^26 - 2756205443/1380983800154112000000*x^25+    + 2756205443/53029777925917900800*x^24 - 2756205443/2301639666923520000*x^23 ++    63392725189/2601853536522240000*x^22 - 63392725189/145144722078720000*x^21 + 63392725189/9215537909760000*x^20+    - 2185956041/23038844774400*x^19 + 41533164779/36377123328000*x^18 - 1339779509/112275072000*x^17+    + 22776251653/211341312000*x^16 - 22776251653/27243216000*x^15 + 1339779509/242161920*x^14+    - 1339779509/43243200*x^13 + 17417133617/119750400*x^12 - 470733341/831600*x^11+    + 272529829/151200*x^10 - 20963833/4536*x^9 + 20963833/2240*x^8 - 511313/35*x^7+    + 511313/30*x^6 - 71346/5*x^5 + 16215/2*x^4 - 8648/3*x^3 + 564*x^2 - 48*x + 1+  '49': -1/608281864034267560872252163321295376887552831379210240000000000*x^49 ++    1/253345216174205564711475286681089286500438497034240000000000*x^48 - 1/219917722373442330478711186355112227864963973120000000000*x^47     + 47/14037301428092063647577309767347589012657274880000000000*x^46 - 47/26535541451969874570089432452452909286686720000000000*x^45     + 47/65519855436962653259480080129513356263424000000000*x^44 - 47/203057403213727231176074628500557922304000000000*x^43

from line 439 (6 lines, 2 fewer than before) @@ -539,8 +439,6 @@

     + 582659/30*x^6 - 158907/10*x^5 + 52969/6*x^4 - 9212/3*x^3 + 588*x^2 - 49*x +     1-- params:-    n: '50'-  number: 1/30414093201713378043612608166064768844377641568960512000000000000*x^50-    - 1/12165637280685351217445043266425907537751056627584204800000000*x^49 + 1/10133808646968222588459011467243571460017539881369600000000*x^48+  '50': 1/30414093201713378043612608166064768844377641568960512000000000000*x^50 -+    1/12165637280685351217445043266425907537751056627584204800000000*x^49 + 1/10133808646968222588459011467243571460017539881369600000000*x^48     - 1/13195063342406539828722671181306733671897838387200000000*x^47 + 47/1122984114247365091806184781387807121012581990400000000*x^46     - 47/2653554145196987457008943245245290928668672000000000*x^45 + 47/7862382652435518391137609615541602751610880000000*x^44