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 A146162 Expansion of eta(q^2)^2 * eta(q^5) / (eta(q) * eta(q^4)^2) in powers of q. 3

%I

%S 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 30,0,38,84,48,0,57,126,68,0,84,184,102,0,121,264,143,0,172,376,207,0,

%U 243,528,284,0,338,732,400,0,465,1008,542,0,636,1374,744,0,862,1856,996,0

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

%H G. C. Greubel, <a href="/A146162/b146162.txt">Table of n, a(n) for n = 0..1000</a>

%F 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 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 a(4*n + 2) = 0.

%e 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 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 (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 A138526(n) = a(4*n). A145722(n) = a(4*n + 1). A146163(n) = a(4*n + 3).

%K nonn

%O 0,5

%A _Michael Somos_, Oct 27 2008

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Last modified September 24 03:26 EDT 2021. Contains 347623 sequences. (Running on oeis4.)