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%I #7 May 26 2018 13:00:20
%S 0,0,1,1,2,3,7,9,14,20,32,43,63,85,122,162,221,292,396,514,680,878,
%T 1147,1465,1886,2391,3050,3836,4841,6048,7579,9403,11685,14419,17806,
%U 21845,26810,32725,39947,48528,58926,71267,86151,103750,124860,149791,179551
%N G.f.: Sum_{k>=1} x^(2*k)/(1+x^(2*k)) * Product_{k>=1} 1/(1-x^k).
%H Vaclav Kotesovec, <a href="/A305121/b305121.txt">Table of n, a(n) for n = 0..10000</a>
%F For n > 0, a(n) = A209423(n) - A305123(n).
%F a(n) ~ log(2) * exp(Pi*sqrt(2*n/3)) / (2^(5/2)*Pi*sqrt(n)).
%t nmax = 60; CoefficientList[Series[Sum[x^(2*k)/(1+x^(2*k)), {k, 1, nmax}] * Product[1/(1-x^k), {k, 1, nmax}], {x, 0, nmax}], x]
%Y Cf. A006128, A209423, A066898, A066897, A305123.
%Y Cf. A116680, A305122.
%K nonn
%O 0,5
%A _Vaclav Kotesovec_, May 26 2018
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