A316462 Expansion of Product_{k>=1} 1/(1-x^k)^(10*k).

1, 10, 75, 450, 2365, 11202, 49020, 200900, 779650, 2886970, 10263057, 35193340, 116865525, 376994900, 1184596410, 3633899268, 10904012980, 32058245900, 92484729375, 262142323480, 730865120997, 2006375900880, 5428232646875, 14485462366250, 38155463010810

Offset

0,2

Links

Alois P. Heinz, Table of n, a(n) for n = 0..5000

Formula

a(n) ~ 2^(7/18) * 5^(4/9) * exp(5/6 + 3 * 2^(-1/3) * 5^(1/3) * zeta(3)^(1/3) * n^(2/3)) * zeta(3)^(4/9) / (A^10 * sqrt(3*Pi) * n^(17/18)), where A is the Glaisher-Kinkelin constant (A074962). - Vaclav Kotesovec, Jun 09 2026

Crossrefs

Column k=10 of A255961.

Sequence in context: A274251 A073379 A283238 * A022734 A027203 A291003

Adjacent sequences: A316459 A316460 A316461 * A316463 A316464 A316465

Keyword

nonn

Author

Seiichi Manyama, Jul 04 2018

Status

approved