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%I #21 Dec 21 2015 12:30:52
%S 1,1,3,7,16,36,79,171,367,776,1625,3379,6969,14262,29001,58644,117951,
%T 235994,469904,931642,1839708,3618893,7092676,13853271,26970933,
%U 52350092,101316743,195544281,376411466,722747148,1384416306,2645765058,5045240163,9600533209,18231674112,34554871809,65369632350,123440337791
%N Expansion of 1/Product_{n>=1} (1 - (q + q^2)^n).
%C What does this sequence count?
%H Vaclav Kotesovec, <a href="/A238441/b238441.txt">Table of n, a(n) for n = 0..4400</a>
%F G.f.: 1/Product_{n>=1} (1 - (q + q^2)^n).
%F G.f.: P(x+x^2), where P(x) is g.f. of A000041, a(n) = Sum_{k=0..n} binomial(k,n-k)*p(k), where p(n) is number of partitions n. - _Vladimir Kruchinin_, Dec 21 2015
%F a(n) ~ phi^n * exp(Pi*sqrt(2*phi*n/(3*sqrt(5))) + Pi^2/(60*phi)) / (4*sqrt(3)*n), where phi = A001622 = (1+sqrt(5))/2 is the golden ratio. - _Vaclav Kotesovec_, Dec 21 2015
%t nmax=40; CoefficientList[Series[Product[1/(1 - (x+x^2)^k), {k, 1, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Dec 21 2015 *)
%o (PARI) q = 'q + O('q^66); Vec(1/eta(q*(1+q)))
%Y Cf. A266108, A266124.
%K nonn
%O 0,3
%A _Joerg Arndt_, Feb 27 2014
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