Where each entry of Touchard polynomials $T_n$ came from

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41 entries.

n value last changed by
0 1 2026-08-26 — bmatschke (run TouchardPolynomials-1787754880)
1 x 2026-08-26 — bmatschke (run TouchardPolynomials-1787754880)
2 x^2 + x 2026-08-26 — bmatschke (run TouchardPolynomials-1787754880)
3 x^3 + 3*x^2 + x 2026-08-26 — bmatschke (run TouchardPolynomials-1787754880)
4 x^4 + 6*x^3 + 7*x^2 + x 2026-08-26 — bmatschke (run TouchardPolynomials-1787754880)
5 x^5 + 10*x^4 + 25*x^3 + 15*x^2 + x 2026-08-26 — bmatschke (run TouchardPolynomials-1787754880)
6 x^6 + 15*x^5 + 65*x^4 + 90*x^3 + 31*x^2 + x 2026-08-26 — bmatschke (run TouchardPolynomials-1787754880)
7 x^7 + 21*x^6 + 140*x^5 + 350*x^4 + 301*x^3 + 63*x^2 + x 2026-08-26 — bmatschke (run TouchardPolynomials-1787754880)
8 x^8 + 28*x^7 + 266*x^6 + 1050*x^5 + 1701*x^4 + 966*x^3 + 127*x^2 + x 2026-08-26 — bmatschke (run TouchardPolynomials-1787754880)
9 x^9 + 36*x^8 + 462*x^7 + 2646*x^6 + 6951*x^5 + 7770*x^4 + 3025*x^3 + … 2026-08-26 — bmatschke (run TouchardPolynomials-1787754880)
10 x^10 + 45*x^9 + 750*x^8 + 5880*x^7 + 22827*x^6 + 42525*x^5 + 34105*x^… 2026-08-26 — bmatschke (run TouchardPolynomials-1787754880)
11 x^11 + 55*x^10 + 1155*x^9 + 11880*x^8 + 63987*x^7 + 179487*x^6 + 2467… 2026-08-26 — bmatschke (run TouchardPolynomials-1787754880)
12 x^12 + 66*x^11 + 1705*x^10 + 22275*x^9 + 159027*x^8 + 627396*x^7 + 13… 2026-08-26 — bmatschke (run TouchardPolynomials-1787754880)
13 x^13 + 78*x^12 + 2431*x^11 + 39325*x^10 + 359502*x^9 + 1899612*x^8 + … 2026-08-26 — bmatschke (run TouchardPolynomials-1787754880)
14 x^14 + 91*x^13 + 3367*x^12 + 66066*x^11 + 752752*x^10 + 5135130*x^9 +… 2026-08-26 — bmatschke (run TouchardPolynomials-1787754880)
15 x^15 + 105*x^14 + 4550*x^13 + 106470*x^12 + 1479478*x^11 + 12662650*x… 2026-08-26 — bmatschke (run TouchardPolynomials-1787754880)
16 x^16 + 120*x^15 + 6020*x^14 + 165620*x^13 + 2757118*x^12 + 28936908*x… 2026-08-26 — bmatschke (run TouchardPolynomials-1787754880)
17 x^17 + 136*x^16 + 7820*x^15 + 249900*x^14 + 4910178*x^13 + 62022324*x… 2026-08-26 — bmatschke (run TouchardPolynomials-1787754880)
18 x^18 + 153*x^17 + 9996*x^16 + 367200*x^15 + 8408778*x^14 + 125854638*… 2026-08-26 — bmatschke (run TouchardPolynomials-1787754880)
19 x^19 + 171*x^18 + 12597*x^17 + 527136*x^16 + 13916778*x^15 + 24357753… 2026-08-26 — bmatschke (run TouchardPolynomials-1787754880)
20 x^20 + 190*x^19 + 15675*x^18 + 741285*x^17 + 22350954*x^16 + 45232920… 2026-08-26 — bmatschke (run TouchardPolynomials-1787754880)
21 x^21 + 210*x^20 + 19285*x^19 + 1023435*x^18 + 34952799*x^17 + 8099444… 2026-08-26 — bmatschke (run TouchardPolynomials-1787754880)
22 x^22 + 231*x^21 + 23485*x^20 + 1389850*x^19 + 53374629*x^18 + 1404142… 2026-08-26 — bmatschke (run TouchardPolynomials-1787754880)
23 x^23 + 253*x^22 + 28336*x^21 + 1859550*x^20 + 79781779*x^19 + 2364885… 2026-08-26 — bmatschke (run TouchardPolynomials-1787754880)
24 x^24 + 276*x^23 + 33902*x^22 + 2454606*x^21 + 116972779*x^20 + 388073… 2026-08-26 — bmatschke (run TouchardPolynomials-1787754880)
25 x^25 + 300*x^24 + 40250*x^23 + 3200450*x^22 + 168519505*x^21 + 622019… 2026-08-26 — bmatschke (run TouchardPolynomials-1787754880)
26 x^26 + 325*x^25 + 47450*x^24 + 4126200*x^23 + 238929405*x^22 + 975910… 2026-08-26 — bmatschke (run TouchardPolynomials-1787754880)
27 x^27 + 351*x^26 + 55575*x^25 + 5265000*x^24 + 333832005*x^23 + 150155… 2026-08-26 — bmatschke (run TouchardPolynomials-1787754880)
28 x^28 + 378*x^27 + 64701*x^26 + 6654375*x^25 + 460192005*x^24 + 226936… 2026-08-26 — bmatschke (run TouchardPolynomials-1787754880)
29 x^29 + 406*x^28 + 74907*x^27 + 8336601*x^26 + 626551380*x^25 + 337382… 2026-08-26 — bmatschke (run TouchardPolynomials-1787754880)
30 x^30 + 435*x^29 + 86275*x^28 + 10359090*x^27 + 843303006*x^26 + 49402… 2026-08-26 — bmatschke (run TouchardPolynomials-1787754880)
31 x^31 + 465*x^30 + 98890*x^29 + 12774790*x^28 + 1122998436*x^27 + 7132… 2026-08-26 — bmatschke (run TouchardPolynomials-1787754880)
32 x^32 + 496*x^31 + 112840*x^30 + 15642600*x^29 + 1480692556*x^28 + 101… 2026-08-26 — bmatschke (run TouchardPolynomials-1787754880)
33 x^33 + 528*x^32 + 128216*x^31 + 19027800*x^30 + 1934327956*x^29 + 143… 2026-08-26 — bmatschke (run TouchardPolynomials-1787754880)
34 x^34 + 561*x^33 + 145112*x^32 + 23002496*x^31 + 2505161956*x^30 + 199… 2026-08-26 — bmatschke (run TouchardPolynomials-1787754880)
35 x^35 + 595*x^34 + 163625*x^33 + 27646080*x^32 + 3218239332*x^31 + 274… 2026-08-26 — bmatschke (run TouchardPolynomials-1787754880)
36 x^36 + 630*x^35 + 183855*x^34 + 33045705*x^33 + 4102913892*x^32 + 374… 2026-08-26 — bmatschke (run TouchardPolynomials-1787754880)
37 x^37 + 666*x^36 + 205905*x^35 + 39296775*x^34 + 5193422157*x^33 + 505… 2026-08-26 — bmatschke (run TouchardPolynomials-1787754880)
38 x^38 + 703*x^37 + 229881*x^36 + 46503450*x^35 + 6529512507*x^34 + 676… 2026-08-26 — bmatschke (run TouchardPolynomials-1787754880)
39 x^39 + 741*x^38 + 255892*x^37 + 54779166*x^36 + 8157133257*x^35 + 898… 2026-08-26 — bmatschke (run TouchardPolynomials-1787754880)
40 x^40 + 780*x^39 + 284050*x^38 + 64247170*x^37 + 10129183233*x^36 + 11… 2026-08-26 — bmatschke (run TouchardPolynomials-1787754880)