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

0, 1, 65, 47449, 194397760, 3037656102976, 141727869124448256, 16674281388691716870144, 4371079210518164503303028736, 2322975003299339366419974718488576, 2322977286679362958150790503464960000000

Offset

0,3

Links

Seiichi Manyama, Table of n, a(n) for n = 0..104

Formula

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

a(n) ~ 8 * Pi^9 * n^(6*n+3) / (945 * exp(6*n)). - Vaclav Kotesovec, Aug 27 2017

a(n) = (n!)^6 * A103345(n)/A103346(n). - Petros Hadjicostas, May 10 2020

Sum_{n>=0} a(n) * x^n / (n!)^6 = polylog(6,x) / (1 - x). - Ilya Gutkovskiy, Jul 15 2020

Mathematica

Table[(n!)^6 * Sum[1/i^6, {i, 1, n}], {n, 0, 15}] (* Vaclav Kotesovec, Aug 27 2017 *)

Crossrefs

Column k=6 of A291556.

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

Cf. A008516, A103345, A103346.

Sequence in context: A219564 A183238 A103345 * A269794 A242283 A061688

Adjacent sequences: A291453 A291454 A291455 * A291457 A291458 A291459

Keyword

nonn

Author

Seiichi Manyama, Aug 24 2017

Status

approved