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%I #15 Jan 05 2021 05:37:07
%S 1,1,2,4,6,9,15,21,31,46,64,89,126,170,231,314,417,552,733,955,1244,
%T 1617,2079,2665,3413,4331,5485,6931,8704,10901,13629,16949,21033,
%U 26045,32123,39529,48553,59429,72599,88518,107624,130599,158209,191175,230611,277717,333730,400375,479598,573386,684481
%N Expansion of Product_{k>=1} (1 + x^(3*k)) / (1 - x^k).
%H Vaclav Kotesovec, <a href="/A266648/b266648.txt">Table of n, a(n) for n = 0..5000</a>
%H Wenjie Fang, Hsien-Kuei Hwang, and Mihyun Kang, <a href="https://arxiv.org/abs/2004.08901">Phase transitions from exp(n^(1/2)) to exp(n^(2/3)) in the asymptotics of banded plane partitions</a>, arXiv:2004.08901 [math.CO], 2020, p. 6.
%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], 2015-2016.
%F a(n) ~ sqrt(7) * exp(sqrt(7*n)*Pi/3) / (24*n).
%t nmax = 50; CoefficientList[Series[Product[(1+x^(3*k))/(1-x^k), {k, 1, nmax}], {x, 0, nmax}], x]
%Y Cf. A000726, A015128, A100405, A266647, A266649, A266650, A285445, A285447.
%K nonn
%O 0,3
%A _Vaclav Kotesovec_, Jan 02 2016
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