A316461 Expansion of Product_{k>=1} 1/(1-x^k)^(9*k).

1, 9, 63, 354, 1755, 7866, 32682, 127458, 471681, 1668313, 5673501, 18635229, 59342520, 183768255, 554843493, 1636855647, 4727195028, 13386032649, 37219413972, 101741003451, 273721954086, 725498278359, 1896086574252, 4890111992460, 12454590256587

Offset

0,2

Links

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

Formula

a(n) ~ 2^(-1/12) * 3^(1/3) * exp(3/4 + 2^(-2/3) * 3^(5/3) * zeta(3)^(1/3) * n^(2/3)) * zeta(3)^(5/12) / (A^9 * sqrt(Pi) * n^(11/12)), where A is the Glaisher-Kinkelin constant (A074962). - Vaclav Kotesovec, Jun 09 2026

Crossrefs

Column k=9 of A255961.

Sequence in context: A015669 A202982 A073378 * A022733 A111997 A016137

Adjacent sequences: A316458 A316459 A316460 * A316462 A316463 A316464

Keyword

nonn

Author

Seiichi Manyama, Jul 04 2018

Status

approved