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%I #10 May 21 2018 07:48:27
%S 1,0,0,2,0,4,4,8,4,20,20,28,38,52,80,128,128,176,300,316,476,648,832,
%T 972,1428,1720,2340,3014,3844,4588,6556,7476,9760,12588,15596,19480,
%U 25140,29796,37728,47604,58140,70856,90148,107692,133228,167284,198692,242728
%N G.f.: Sum_{k>=0} q(k)^2 * x^k / Sum_{k>=0} q(k)*x^k, where q(n) is A000009(n).
%H Seiichi Manyama, <a href="/A304877/b304877.txt">Table of n, a(n) for n = 0..10000</a>
%F a(n) ~ sqrt(3) * exp(Pi*sqrt(n)) / (2^(11/2) * n^(3/2)).
%t nmax = 50; CoefficientList[Series[Sum[PartitionsQ[k]^2*x^k, {k, 0, nmax}] / Sum[PartitionsQ[k]*x^k, {k, 0, nmax}], {x, 0, nmax}], x]
%Y Cf. A000009, A054440, A304873, A304878.
%K nonn
%O 0,4
%A _Vaclav Kotesovec_, May 20 2018
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