A291505 a(n) = (n!)^7 * Sum_{i=1..n} 1/i^7.

0, 1, 129, 282251, 4624680320, 361307736471424, 101143400834944548864, 83296040059942781485105152, 174684539610200377980575079727104, 835510910973061065615656036610946891776, 8355109938323553617123838798161699143680000000

Offset: 0

Author

Seiichi Manyama, Aug 25 2017

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..92

Crossrefs

Cf. A000254 (k=1), A001819 (k=2), A066989 (k=3), A099827 (k=5), A291456 (k=6), this sequence (k=7), A291506 (k=8), A291507 (k=9), A291508 (k=10).

Column k=7 of A291556.

Programs

Mathematica

Table[(n!)^7 * Sum[1/i^7, {i, 1, n}], {n, 0, 15}] (* Vaclav Kotesovec, Aug 27 2017 *)

PARI

a(n) = n!^7*sum(i=1, n, 1/i^7); \\ Michel Marcus, Aug 26 2017

Formula

a(0) = 0, a(1) = 1, a(n+1) = (n^7+(n+1)^7)*a(n) - n^14*a(n-1) for n > 0.

a(n) ~ zeta(7) * (2*Pi)^(7/2) * n^(7*n+7/2) / exp(7*n). - Vaclav Kotesovec, Aug 27 2017

Sum_{n>=0} a(n) * x^n / (n!)^7 = polylog(7,x) / (1 - x). - Ilya Gutkovskiy, Jul 15 2020