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A291456 a(n) = (n!)^6 * Sum_{i=1..n} 1/i^6. 6
0, 1, 65, 47449, 194397760, 3037656102976, 141727869124448256, 16674281388691716870144, 4371079210518164503303028736, 2322975003299339366419974718488576, 2322977286679362958150790503464960000000 (list; graph; refs; listen; history; text; internal format)
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

MATHEMATICA

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

CROSSREFS

Cf. A000254 (k=1), A001819 (k=2), A066989 (k=3), A099827 (k=5), this sequence (k=6).

Cf. A008516.

Column k=6 of A291556.

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

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Last modified February 29 02:07 EST 2020. Contains 332353 sequences. (Running on oeis4.)