A291506 a(n) = (n!)^8 * Sum_{i=1..n} 1/i^8.

0, 1, 257, 1686433, 110523752704, 43173450975314176, 72514862031522895036416, 418033821374598847702425993216, 7013444132843374500928464765799366656, 301905779820559925981495987360836056017534976

Offset: 0

Author

Seiichi Manyama, Aug 25 2017

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..83

Crossrefs

Cf. A000254 (k=1), A001819 (k=2), A066989 (k=3), A099827 (k=5), A291456 (k=6), A291505 (k=7), this sequence (k=8), A291507 (k=9), A291508 (k=10).

Column k=8 of A291556.

Programs

Mathematica

Table[(n!)^8 * Sum[1/i^8, {i, 1, n}], {n, 0, 15}] (* Vaclav Kotesovec, Aug 27 2017 *)

PARI

a(n) = n!^8*sum(i=1, n, 1/i^8); \\ Michel Marcus, Aug 26 2017

Formula

a(0) = 0, a(1) = 1, a(n+1) = (n^8+(n+1)^8)*a(n) - n^16*a(n-1) for n > 0.

a(n) ~ 8 * Pi^12 * n^(8*n+4) / (4725 * exp(8*n)). - Vaclav Kotesovec, Aug 27 2017

Sum_{n>=0} a(n) * x^n / (n!)^8 = polylog(8,x) / (1 - x). - Ilya Gutkovskiy, Jul 15 2020