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%I #35 Mar 22 2018 12:35:34
%S 1,0,1,-1,2,-1,2,-2,4,-3,5,-5,8,-7,10,-10,15,-14,19,-20,27,-26,34,-36,
%T 47,-47,59,-63,79,-81,99,-106,130,-135,162,-174,208,-219,258,-278,328,
%U -347,404,-436,507,-540,621,-671,772,-825,941,-1017,1159,-1242,1405
%N Expansion of Product_{k>=1} (1-x^(3*k))/(1-x^(2*k)).
%H Vaclav Kotesovec, <a href="/A262346/b262346.txt">Table of n, a(n) for n = 0..10000</a>
%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, p. 15.
%F a(n) ~ (-1)^n * 5^(1/4) * exp(Pi*sqrt(5*n/2)/3) / (3 * 2^(7/4) * n^(3/4)).
%e G.f. = 1 + x^2 - x^3 + 2*x^4 - x^5 + 2*x^6 - 2*x^7 + 4*x^8 - 3*x^9 + 5*x^10 + ...
%t nmax = 60; CoefficientList[Series[Product[(1-x^(3*k))/(1-x^(2*k)), {k, 1, nmax}], {x, 0, nmax}], x]
%t CoefficientList[Series[QPochhammer[x^3]/QPochhammer[x^2], {x, 0, 60}], x]
%o (PARI) lista(nn) = {q='q+O('q^nn); Vec(eta(q^3)/eta(q^2))} \\ _Altug Alkan_, Mar 21 2018
%Y Cf. A000726, A007690, A262151, A262364.
%K sign
%O 0,5
%A _Vaclav Kotesovec_, Sep 23 2015
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