A291505 - OEIS

%I #24 Jul 15 2020 10:13:09

%S 0,1,129,282251,4624680320,361307736471424,101143400834944548864,

%T 83296040059942781485105152,174684539610200377980575079727104,

%U 835510910973061065615656036610946891776,8355109938323553617123838798161699143680000000

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

%H Seiichi Manyama, <a href="/A291505/b291505.txt">Table of n, a(n) for n = 0..92</a>

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

%F a(n) ~ zeta(7) * (2*Pi)^(7/2) * n^(7*n+7/2) / exp(7*n). - _Vaclav Kotesovec_, Aug 27 2017

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

%t Table[(n!)^7 * Sum[1/i^7, {i, 1, n}], {n, 0, 15}] (* _Vaclav Kotesovec_, Aug 27 2017 *)

%o (PARI) a(n) = n!^7*sum(i=1, n, 1/i^7); \\ _Michel Marcus_, Aug 26 2017

%Y 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).

%Y Column k=7 of A291556.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Aug 25 2017