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A291456 a(n) = (n!)^6 * Sum_{i=1..n} 1/i^6. 8

%I

%S 0,1,65,47449,194397760,3037656102976,141727869124448256,

%T 16674281388691716870144,4371079210518164503303028736,

%U 2322975003299339366419974718488576,2322977286679362958150790503464960000000

%N a(n) = (n!)^6 * Sum_{i=1..n} 1/i^6.

%H Seiichi Manyama, <a href="/A291456/b291456.txt">Table of n, a(n) for n = 0..104</a>

%F a(0) = 0, a(1) = 1, a(n+1) = (n^6 + (n+1)^6)*a(n) - n^12*a(n-1) for n > 0.

%F a(n) ~ 8 * Pi^9 * n^(6*n+3) / (945 * exp(6*n)). - _Vaclav Kotesovec_, Aug 27 2017

%F a(n) = (n!)^6 * A103345(n)/A103346(n). - _Petros Hadjicostas_, May 10 2020

%t Table[(n!)^6 * Sum[1/i^6, {i, 1, n}], {n, 0, 15}] (* _Vaclav Kotesovec_, Aug 27 2017 *)

%Y Column k=6 of A291556.

%Y Cf. A000254 (k=1), A001819 (k=2), A066989 (k=3), A203229 (k=4), A099827 (k=5).

%Y Cf. A008516, A103345, A103346.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Aug 24 2017

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Last modified July 9 14:08 EDT 2020. Contains 335543 sequences. (Running on oeis4.)