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%I #8 Jul 11 2016 08:25:39
%S 0,1,2,5,8,16,28,48,78,124,194,302,454,682,996,1457,2096,2993,4226,
%T 5920,8228,11373,15580,21246,28740,38731,51872,69155,91716,121105,
%U 159208,208512,271894,353338,457336,590124,758792,972677,1242896,1583576
%N Expansion of (eta(q^3)eta(q^15)/(eta(q)eta(q^5)))^2 in powers of q.
%C Euler transform of period 15 sequence [2,2,0,2,4,0,2,2,0,4,2,0,2,2,0,...].
%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.
%F G.f. A(x) satisfies 0=f(A(x), A(x^2)) where f(u, v)=u^3+v^3-4uv(u+v)-9u^2v^2-uv.
%F a(n) ~ exp(4*Pi*sqrt(n/15)) / (9*sqrt(2)*15^(1/4)*n^(3/4)). - _Vaclav Kotesovec_, Jul 11 2016
%t nmax = 50; CoefficientList[Series[x*Product[((1-x^(3*k)) * (1-x^(15*k)) / ((1-x^k) * (1-x^(5*k))))^2, {k, 1, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Jul 11 2016 *)
%o (PARI) {a(n)=local(A); if(n<1, 0, n--; A=x*O(x^n); polcoeff((eta(x^3+A)*eta(x^15+A)/eta(x+A)/eta(x^5+A))^2,n))}
%o (PARI) {a(n)=local(A, u, v); if(n<0, 0, A=x; for(k=2, n, u=A+x*O(x^k); v=subst(u, x, x^2); A-=x^k*polcoeff(u^3+v^3-4*u*v*(u+v)-9*u^2*v^2-u*v, k+2)/2); polcoeff(A, n))}
%K nonn
%O 0,3
%A _Michael Somos_, Mar 17 2004
%E Changed offset to 0 and added a(0)=0 by _Vaclav Kotesovec_, Jul 11 2016
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