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%I #12 Oct 09 2024 10:41:51
%S 1,1,4,9,16,28,49,84,140,228,361,560,856,1288,1916,2821,4108,5928,
%T 8480,12024,16920,23637,32788,45196,61928,84368,114332,154160,206857,
%U 276308,367476,486680,641996,843656,1104592,1441168,1873965,2428816,3138132,4042408,5192132
%N G.f.: Sum_{k>=0} x^(k*(k+1)/2) * Product_{j=1..k} ((1 + x^j)/(1 - x^j))^2.
%H Vaclav Kotesovec, <a href="/A376853/b376853.txt">Table of n, a(n) for n = 0..10000</a>
%F a(n) ~ c * exp(sqrt(8*n*(log(r)^2 + polylog(2,r) - polylog(2,-r)))), where r = A192918 = 0.54368901269207636157... is the real root of the equation r*(1+r^2) = (1-r^2) and c = 0.0643033662740307713580663125340126524175...
%t nmax = 60; CoefficientList[Series[Sum[x^(k*(k+1)/2) * Product[(1+x^j)/(1-x^j), {j, 1, k}]^2, {k, 0, Sqrt[2*nmax]}], {x, 0, nmax}], x]
%Y Cf. A001935, A143184, A192918, A376812, A376852, A376854.
%K nonn
%O 0,3
%A _Vaclav Kotesovec_, Oct 06 2024