%I #12 Sep 07 2023 15:52:31

%S 1,1,33,276,2324,13225,145586,760057,6836328,45996924,322816122,

%T 2064921330,16881567137,96217644312,708147553326,4769313137735,

%U 31412238427954,198869428043476,1442034056253438,8596120396405880,58954590481229064,387170921610808720

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

%H Vaclav Kotesovec, <a href="/A265839/b265839.txt">Table of n, a(n) for n = 0..1240</a>

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

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

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

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

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

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

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

%Y Column k=5 of A292193.

%K nonn

%O 0,3

%A _Vaclav Kotesovec_, Dec 16 2015