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%I #14 Oct 01 2015 02:17:30
%S 1,4,16,60,208,692,2224,6940,21152,63188,185488,536268,1529648,
%T 4310804,12017264,33171916,90745472,246201412,662897232,1772295020,
%U 4707336848,12426673188,32617079280,85152717404,221183486496,571784014244,1471463190032,3770577250716
%N Expansion of Product_{k>=1} ((1+x^k)/(1-x^k))^(2^k).
%C Convolution of A034899 and A102866.
%H Vaclav Kotesovec, <a href="/A261519/b261519.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]
%H Vaclav Kotesovec, <a href="http://arxiv.org/abs/1509.08708">A method of finding the asymptotics of q-series based on the convolution of generating functions</a>, arXiv:1509.08708 [math.CO], Sep 30 2015, p. 27.
%F a(n) ~ 2^n * exp(2*sqrt(2*n) - 1 + c) / (sqrt(Pi) * 2^(3/4) * n^(3/4)), where c = 2 * Sum_{j>=1} 1/((2*j+1)*(2^(2*j)-1)) = 0.2545212486386431009939814261118792033...
%t nmax = 40; CoefficientList[Series[Product[((1 + x^k)/(1 - x^k))^(2^k), {k, 1, nmax}], {x, 0, nmax}], x]
%Y Cf. A156616, A261520, A260916, A001934, A015128.
%K nonn
%O 0,2
%A _Vaclav Kotesovec_, Aug 23 2015
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