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%I #14 Oct 01 2015 02:17:51
%S 1,6,36,200,1038,5160,24776,115632,527172,2355998,10349448,44783064,
%T 191211512,806737800,3367294320,13918479872,57020736942,231697484304,
%U 934399998412,3742041461976,14888854356840,58881590423856,231542984619720,905666813058384
%N Expansion of Product_{k>=1} ((1+x^k)/(1-x^k))^(3^k).
%C Convolution of A144067 and A256142.
%C In general, for m > 1, if g.f. = Product_{k>=1} ((1+x^k)/(1-x^k))^(m^k), then a(n) ~ m^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)*(m^(2*j)-1)).
%H Vaclav Kotesovec, <a href="/A261520/b261520.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) ~ 3^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)*(3^(2*j)-1)) = 0.0887630729103166089354170592729856346...
%t nmax = 40; CoefficientList[Series[Product[((1 + x^k)/(1 - x^k))^(3^k), {k, 1, nmax}], {x, 0, nmax}], x]
%Y Cf. A156616, A261519, A260916, A001934, A015128.
%K nonn
%O 0,2
%A _Vaclav Kotesovec_, Aug 23 2015
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