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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
OFFSET
0,3
LINKS
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
Sum_{n>=0} a(n) * x^n / (n!)^10 = polylog(10,x) / (1 - x). - Ilya Gutkovskiy, Jul 15 2020
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 * A371982 A031530 A004607
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Aug 25 2017
STATUS
approved