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%I #16 Aug 09 2018 00:00:09
%S 1,-3,0,5,0,-9,20,0,-45,0,36,-18,0,135,0,-104,-153,0,-60,0,252,367,0,
%T -450,0,-270,108,0,660,0,-624,-756,0,405,0,2106,-220,0,-900,0,-1188,
%U -63,0,-765,0,-1589,3792,0,925,0,216,-878,0,1260,0,660,-6930,0
%N Expansion of eta(q)^3 * eta(q^5)^9 in powers of q.
%H G. C. Greubel, <a href="/A227901/b227901.txt">Table of n, a(n) for n = 2..2500</a>
%F Euler transform of period 5 sequence [-3, -3, -3, -3, -12, ...].
%F G.f. is a period 1 Fourier series which satisfies f(-1 / (5 t)) = 5^(3/2) (t/i)^6 g(t) where q = exp(2 Pi i t) and g() is the g.f. for A227900.
%F G.f.: x^2 * Product_{k>0} (1 - x^k)^3 * (1 - x^(5*k))^9.
%e G.f. = q^2 - 3*q^3 + 5*q^5 - 9*q^7 + 20*q^8 - 45*q^10 + 36*q^12 - 18*q^13 + ...
%t a[ n_] := SeriesCoefficient[ q^2 QPochhammer[ q]^3 QPochhammer[ q^5]^9, {q, 0, n}];
%o (PARI) {a(n) = my(A); if( n<2, 0, n-=2; A = x * O(x^n); polcoeff( (eta(x + A) * eta(x^5 + A)^3)^3, n))};
%Y Cf. A227900.
%K sign
%O 2,2
%A _Michael Somos_, Oct 15 2013
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