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%I #30 Jul 15 2020 11:36:13
%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
%F Sum_{n>=0} a(n) * x^n / (n!)^6 = polylog(6,x) / (1 - x). - _Ilya Gutkovskiy_, Jul 15 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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