The OEIS is supported by the many generous donors to the OEIS Foundation.
%I #7 May 28 2015 03:38:33
%S 1,2,7,24,65,184,487,1254,3145,7706,18480,43490,100692,229472,515802,
%T 1144416,2508948,5439642,11671859,24801738,52221911,109013538,
%U 225718717,463769652,945915199,1915895576,3854803572,7706786958,15314564282,30255672820,59440488874
%N Expansion of Product_{k>=1} (1+x^k)^(k*(k+1)).
%H Vaclav Kotesovec, <a href="/A258341/b258341.txt">Table of n, a(n) for n = 0..1000</a>
%F a(n) ~ 7^(1/8) / (2^(47/24) * 15^(1/8) * n^(5/8)) * exp(2025*Zeta(3)^3 / (49*Pi^8) - 135*(15/14)^(1/4) * Zeta(3)^2 / (14*Pi^5) * n^(1/4) + 3*sqrt(15/14) * Zeta(3) / Pi^2 * sqrt(n) + 2*(14/15)^(1/4)*Pi/3 * n^(3/4)), where Zeta(3) = A002117.
%t nmax=30; CoefficientList[Series[Product[(1+x^k)^(k*(k+1)),{k,1,nmax}],{x,0,nmax}],x]
%Y Cf. A027998, A028377, A027999, A258342, A258343, A258344, A258345, A258346, A258347.
%K nonn
%O 0,2
%A _Vaclav Kotesovec_, May 27 2015