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%I #11 Jan 05 2016 11:19:57
%S 1,2,4,7,13,21,34,53,82,123,181,263,379,537,754,1047,1444,1972,2675,
%T 3601,4820,6408,8473,11141,14580,18985,24611,31765,40839,52294,66719,
%U 84819,107474,135731,170892,214518,268524,335190,417308,518212,641948,793324,978157
%N Expansion of Product_{k>=1} (1 + x^k - x^(3*k)) / (1 - x^k).
%C Convolution of A266686 and A000041.
%H Vaclav Kotesovec, <a href="/A266650/b266650.txt">Table of n, a(n) for n = 0..5000</a>
%F a(n) ~ sqrt(6*c + Pi^2) * exp(sqrt((4*c + 2*Pi^2/3)*n)) / (4*sqrt(3)*Pi*n), where c = Integral_{0..infinity} log(1 + exp(-x) - exp(-3*x)) dx = 0.59698046904738615106237970379036510874974380079287087827737... . - _Vaclav Kotesovec_, Jan 05 2016
%t nmax = 50; CoefficientList[Series[Product[(1+x^k-x^(3*k))/(1-x^k), {k, 1, nmax}], {x, 0, nmax}], x]
%Y Cf. A000726, A100405, A266647, A266648, A266649, A266686.
%K nonn
%O 0,2
%A _Vaclav Kotesovec_, Jan 02 2016