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%I #21 Feb 02 2017 02:41:24
%S 1,2,4,10,22,48,104,220,460,954,1956,3976,8026,16084,32032,63440,
%T 124974,245008,478204,929452,1799508,3471396,6673724,12788976,
%U 24433528,46546738,88432264,167575474,316768948,597389576,1124092476,2110661644,3955006820,7396477224
%N Expansion of Product_{k>=1} ((1+x^k)/(1-x^k))^(Fibonacci(k)).
%C Convolution of A166861 and A261050.
%H G. C. Greubel, <a href="/A260916/b260916.txt">Table of n, a(n) for n = 0..1000</a>
%H Vaclav Kotesovec, <a href="http://arxiv.org/abs/1508.01796">Asymptotics of the Euler transform of Fibonacci numbers</a>, arXiv:1508.01796 [math.CO], Aug 07 2015.
%F a(n) ~ phi^n / (2^(3/4) * 5^(1/8) * sqrt(Pi) * n^(3/4)) * exp(-1/5 + 2*5^(-1/4)*sqrt(2*n) + s), where s = 2 * Sum_{k>=1} phi^(2*k+1) / ((phi^(4*k+2) - phi^(2*k+1) - 1)*(2*k+1)) = 0.276751423987223411719438512082359840225908317... and phi = A001622 = (1+sqrt(5))/2 is the golden ratio.
%t nmax = 40; CoefficientList[Series[Product[((1+x^k)/(1-x^k))^Fibonacci[k], {k, 1, nmax}], {x, 0, nmax}], x]
%Y Cf. A000045, A001622, A166861, A261050, A261519, A261520.
%K nonn
%O 0,2
%A _Vaclav Kotesovec_, Aug 18 2015
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