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A291508 a(n) = (n!)^10 * Sum_{i=1..n} 1/i^10. 5
0, 1, 1025, 60526249, 63466432537600, 619789443653380965376, 37476298202061058687475122176, 10586126703664512292193022557971021824, 11366767006463449393869821987386636472445566976, 39633465899293694663690352980684333029782095493517541376 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..69

FORMULA

a(0) = 0, a(1) = 1, a(n+1) = (n^10+(n+1)^10)*a(n) - n^20*a(n-1) for n > 0.

a(n) ~ 32 * Pi^15 * n^(10*n+5) / (93555 * exp(10*n)). - Vaclav Kotesovec, Aug 27 2017

MATHEMATICA

Table[(n!)^10 * Sum[1/i^10, {i, 1, n}], {n, 0, 12}] (* Vaclav Kotesovec, Aug 27 2017 *)

PROG

(PARI) a(n) = n!^10*sum(i=1, n, 1/i^10); \\ Michel Marcus, Aug 26 2017

CROSSREFS

Cf. A000254 (k=1), A001819 (k=2), A066989 (k=3), A099827 (k=5), A291456 (k=6), A291505 (k=7), A291506 (k=8), A291507 (k=9), this sequence (k=10).

Column k=10 of A291556.

Sequence in context: A272672 A180270 A103716 * A031530 A004607 A221008

Adjacent sequences:  A291505 A291506 A291507 * A291509 A291510 A291511

KEYWORD

nonn

AUTHOR

Seiichi Manyama, Aug 25 2017

STATUS

approved

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Last modified January 21 05:39 EST 2020. Contains 331104 sequences. (Running on oeis4.)