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%I #9 Jan 04 2016 08:57:18
%S 1,5,11,30,66,115,252,445,762,1350,2238,3690,5909,9480,14460,22475,
%T 34326,51150,76398,111810,163350,236610,339667,482040,684060,960780,
%U 1340953,1863570,2573022,3533310,4830822,6580170,8900382,12011430,16125198,21567965
%N Expansion of Product_{k>=1} ((1 + 2*x^k) * (1 + 3*x^k)).
%C Convolution of A032302 and A032308.
%C In general, for m1 > 0 and m2 > 0, if g.f. = Product_{k>=1} ((1 + m1*x^k) * (1 + m2*x^k)) then a(n) ~ c^(1/4) * exp(2*sqrt(c*n)) / (2*sqrt((m1+1)*(m2+1)*Pi) * n^(3/4)), where c = Pi^2/3 + log(m1)^2/2 + log(m2)^2/2 + polylog(2, -1/m1) + polylog(2, -1/m2).
%H Vaclav Kotesovec, <a href="/A266820/b266820.txt">Table of n, a(n) for n = 0..5000</a>
%F a(n) ~ c^(1/4) * exp(2*sqrt(c*n)) / (4*sqrt(3*Pi) * n^(3/4)), where c = Pi^2/3 + log(2)^2/2 + log(3)^2/2 + polylog(2, -1/2) + polylog(2, -1/3) = 6.665989921346842772385004076363525173910446415877... .
%t nmax = 40; CoefficientList[Series[Product[(1+2*x^k) * (1+3*x^k), {k, 1, nmax}], {x, 0, nmax}], x]
%Y Cf. A032302, A032308, A266819, A266822.
%K nonn
%O 0,2
%A _Vaclav Kotesovec_, Jan 04 2016
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