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%I #11 Mar 12 2021 22:24:48
%S 1,-4,4,0,4,-7,-4,4,4,0,1,-4,4,-4,0,2,-4,0,0,4,2,-4,0,4,0,-1,0,4,-4,
%T -4,-8,0,4,4,4,1,0,0,0,4,-2,0,-4,0,-4,0,-4,0,0,4,2,4,0,-4,-4,8,0,4,0,
%U -4,-1,0,-4,0,0,2,0,-4,4,0,-2,4,-4,0,0,-1,0,0,-4
%N Expansion of phi(-x)^2 / chi(-x^5) in powers of x where psi(), chi() are Ramanujan theta functions.
%C Ramanujan theta functions: f(q) (see A121373), phi(q) (A000122), psi(q) (A010054), chi(q) (A000700).
%H G. C. Greubel, <a href="/A279365/b279365.txt">Table of n, a(n) for n = 0..1000</a>
%H Michael Somos, <a href="/A010815/a010815.txt">Introduction to Ramanujan theta functions</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/RamanujanThetaFunctions.html">Ramanujan Theta Functions</a>
%F Expansion of q^(-5/24) * eta(q)^4 * eta(q^10) / (eta(q^2)^2 * eta(q^5)) in powers of q.
%F Euler transform of period 10 sequence [ -4, -2, -4, -2, -3, -2, -4, -2, -4, -2, ...].
%e G.f. = 1 - 4*x + 4*x^2 + 4*x^4 - 7*x^5 - 4*x^6 + 4*x^7 + 4*x^8 + ...
%e G.f. = q^5 - 4*q^29 + 4*q^53 + 4*q^101 - 7*q^125 - 4*q^149 + ...
%t a[ n_] := SeriesCoefficient[ EllipticTheta[ 4, 0, x]^2 / QPochhammer[ x^5, x^10], {x, 0, n}];
%o (PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x + A)^4 * eta(x^10 + A) / (eta(x^2 + A)^2 * eta(x^5 + A)), n))};
%o (PARI) lista(nn) = {q='q+O('q^nn); Vec(eta(q)^4*eta(q^10)/(eta(q^2)^2*eta(q^5)))} \\ _Altug Alkan_, Mar 21 2018
%K sign
%O 0,2
%A _Michael Somos_, Dec 10 2016
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