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
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
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Aug 25 2017
STATUS
approved