A265839 Expansion of Product_{k>=1} 1/(1 - k^5*x^k).

1, 1, 33, 276, 2324, 13225, 145586, 760057, 6836328, 45996924, 322816122, 2064921330, 16881567137, 96217644312, 708147553326, 4769313137735, 31412238427954, 198869428043476, 1442034056253438, 8596120396405880, 58954590481229064, 387170921610808720

Offset: 0

Author

Vaclav Kotesovec, Dec 16 2015

Keywords

• nonn

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..1240

Crossrefs

Cf. A006906, A077335, A265837, A265838, A265842.

Column k=5 of A292193.

Programs

Mathematica

nmax = 40; CoefficientList[Series[Product[1/(1 - k^5*x^k), {k, 1, nmax}], {x, 0, nmax}], x]

Formula

a(n) ~ c * 3^(5*n/3), where

c = 12.8519823810391431573687005461910113782018563173082562291... if n mod 3 = 0

c = 12.4535903496941652158697054030067622653283880393322526099... if n mod 3 = 1

c = 12.5138855694494734654940524026530463555984202132997900068... if n mod 3 = 2.

G.f.: exp(Sum_{k>=1} Sum_{j>=1} j^(5*k)*x^(j*k)/k). - Ilya Gutkovskiy, Jun 14 2018