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%I #6 Sep 03 2018 15:41:30
%S 1,2,14,44,182,548,1932,5632,17654,49872,145020,395256,1090044,
%T 2876424,7606024,19503312,49850790,124543772,309436980,755268832,
%U 1831194724,4376807896,10387118328,24359228520,56720659372,130737105940,299256890672,678941040784
%N Expansion of Product_{i>=1, j>=1, k>=1} ((1 + x^(i*j*k))/(1 - x^(i*j*k)))^(i*j*k).
%C Convolution of A318413 and A318414.
%H Vaclav Kotesovec, <a href="/A318764/b318764.txt">Table of n, a(n) for n = 0..10000</a>
%F Conjecture: log(a(n)) ~ (21*Zeta(3))^(1/3) * log(n)^(2/3) * n^(2/3) / 2^(5/3).
%t nmax = 40; CoefficientList[Series[Product[Product[Product[((1 + x^(i*j*k))/(1 - x^(i*j*k)))^(i*j*k), {i, 1, nmax/j/k}], {j, 1, nmax/k}], {k, 1, nmax}], {x, 0, nmax}], x]
%t nmax = 40; CoefficientList[Series[Product[((1+x^k)/(1-x^k))^(k*Sum[DivisorSigma[0, d], {d, Divisors[k]}]), {k, 1, nmax}], {x, 0, nmax}], x]
%Y Cf. A318413, A318414.
%Y Cf. A156616, A318579.
%Y Cf. A015128, A305050.
%K nonn
%O 0,2
%A _Vaclav Kotesovec_, Sep 03 2018