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G.f.: Sum_{k>=0} x^(k^2) * Product_{j=1..k} ((1 + x^j)/(1 - x^j))^2.
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%I #8 Oct 08 2024 05:19:57

%S 1,1,4,8,13,20,32,52,84,133,204,304,444,636,900,1264,1761,2440,3364,

%T 4608,6276,8496,11424,15268,20284,26789,35196,46016,59884,77612,

%U 100204,128900,165260,211200,269072,341792,432917,546788,688728,865200,1084048,1354816,1689048

%N G.f.: Sum_{k>=0} x^(k^2) * Product_{j=1..k} ((1 + x^j)/(1 - x^j))^2.

%H Vaclav Kotesovec, <a href="/A376854/b376854.txt">Table of n, a(n) for n = 0..10000</a>

%F a(n) ~ (1 + sqrt(2)) * exp(Pi*sqrt(n)) / (2^(9/2) * n).

%t nmax = 60; CoefficientList[Series[Sum[x^(k^2) * Product[(1+x^j)/(1-x^j), {j, 1, k}]^2, {k, 0, Sqrt[nmax]}], {x, 0, nmax}], x]

%Y Cf. A066447, A000041, A216222, A376852, A376853.

%K nonn

%O 0,3

%A _Vaclav Kotesovec_, Oct 06 2024