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A146162 Expansion of eta(q^2)^2 * eta(q^5) / (eta(q) * eta(q^4)^2) in powers of q.

%I A146162 #8 Dec 05 2017 04:07:18
%S A146162 1,1,0,1,2,1,0,2,4,3,0,3,8,4,0,6,14,8,0,10,22,12,0,16,36,21,0,25,56,
%T A146162 30,0,38,84,48,0,57,126,68,0,84,184,102,0,121,264,143,0,172,376,207,0,
%U A146162 243,528,284,0,338,732,400,0,465,1008,542,0,636,1374,744,0,862,1856,996,0
%N A146162 Expansion of eta(q^2)^2 * eta(q^5) / (eta(q) * eta(q^4)^2) in powers of q.
%H A146162 G. C. Greubel, <a href="/A146162/b146162.txt">Table of n, a(n) for n = 0..1000</a>
%F A146162 Euler transform of period 20 sequence [ 1, -1, 1, 1, 0, -1, 1, 1, 1, -2, 1, 1, 1, -1, 0, 1, 1, -1, 1, 0, ...].
%F A146162 G.f. is a period 1 Fourier series which satisfies f(-1 / (80 t)) = (4/5)^(1/2) g(t) where q = exp(2 Pi i t) and g() is g.f. for A146164.
%F A146162 a(4*n + 2) = 0.
%e A146162 1 + q + q^3 + 2*q^4 + q^5 + 2*q^7 + 4*q^8 + 3*q^9 + 3*q^11 + 8*q^12 + ...
%t A146162 a[n_]:= SeriesCoefficient[QPochhammer[x^5]/(QPochhammer[x]* QPochhammer[ -x^2, x^2]^2), {x, 0, n}]; Table[a[n], {n, 0, 50}] (* _G. C. Greubel_, Dec 04 2017 *)
%o A146162 (PARI) {a(n) = local(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^2 + A)^2 * eta(x^5 + A) / (eta(x + A) * eta(x^4 + A)^2), n))}
%Y A146162 A138526(n) = a(4*n). A145722(n) = a(4*n + 1). A146163(n) = a(4*n + 3).
%K A146162 nonn
%O A146162 0,5
%A A146162 _Michael Somos_, Oct 27 2008