%I #11 Sep 07 2023 15:52:49
%S 1,1,8,35,91,405,1069,3799,8686,36744,86310,235776,686329,1605779,
%T 5230579,13191702,30608501,73907925,206052723,433747560,1324608945,
%U 2995740974,6973434054,15364943439,35816669079,86662644756,184871083828,502089539734,1098571699830
%N Expansion of Product_{k>=1} (1 + k^3*x^k).
%H Vaclav Kotesovec, <a href="/A265840/b265840.txt">Table of n, a(n) for n = 0..2000</a>
%F G.f.: exp(Sum_{k>=1} Sum_{j>=1} (-1)^(k+1)*j^(3*k)*x^(j*k)/k). - _Ilya Gutkovskiy_, Jun 14 2018
%F Conjecture: log(a(n)) ~ 3*sqrt(n/2) * (log(2*n) - 2). - _Vaclav Kotesovec_, Dec 27 2020
%t nmax = 40; CoefficientList[Series[Product[1 + k^3*x^k, {k, 1, nmax}], {x, 0, nmax}], x]
%Y Cf. A022629, A092484, A265837, A265841, A265842.
%Y Column k=3 of A292189.
%K nonn
%O 0,3
%A _Vaclav Kotesovec_, Dec 16 2015