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%I #8 Mar 08 2015 04:20:33
%S 1,4,13,42,117,310,785,1896,4433,10062,22248,48080,101821,211682,
%T 432795,871520,1730491,3391894,6568996,12580316,23841774,44742634,
%U 83193865,153347110,280336704,508499474,915540681,1636805438,2906642396,5128530946,8993376689
%N G.f.: Product_{k>=1} (1+x^k)^(3*k+1).
%H Vaclav Kotesovec, <a href="/A255836/b255836.txt">Table of n, a(n) for n = 0..1000</a>
%F a(n) ~ Zeta(3)^(1/6) * exp(-Pi^4 / (3888*Zeta(3)) + Pi^2 * n^(1/3) / (6^(5/3) * Zeta(3)^(1/3)) + 3^(5/3)/2^(4/3) * Zeta(3)^(1/3) * n^(2/3)) / (2^(17/12) * 3^(1/6) * sqrt(Pi) * n^(2/3)), where Zeta(3) = A002117.
%t nmax=50; CoefficientList[Series[Product[(1+x^k)^(3*k+1),{k,1,nmax}],{x,0,nmax}],x]
%Y Cf. A026007, A219555, A052812, A255271, A255834, A255835, A255837.
%K nonn
%O 0,2
%A _Vaclav Kotesovec_, Mar 07 2015
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