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%I #14 Mar 12 2021 22:24:48
%S 1,0,-4,-1,2,4,8,-2,-5,-9,-4,9,-10,2,8,2,9,-3,1,-5,10,10,-14,-22,-2,7,
%T -9,10,-4,-10,-17,16,18,18,31,-10,10,-20,9,6,-31,-14,0,-9,-28,-23,-7,
%U 36,-8,25,24,-28,18,41,0,6,-13,2,9,5,38,-43,-18,-35,6,-1
%N Expansion of f(-x^2)^4 * psi(-x^3) in powers of x where psi(), f() 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="/A258770/b258770.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^(-17/24) * eta(q^2)^4 * eta(q^3) * eta(q^12) / eta(q^6) in powers of q.
%F Euler transform of period 12 sequence [ 0, -4, -1, -4, 0, -4, 0, -4, -1, -4, 0, -5, ...].
%F G.f.: Product_{k>0} (1 - x^(2*k))^4 * (1 - x^(3*k)) * (1 + x^(6*k)).
%F 16 * a(n) = A258771(3*n + 2).
%e G.f. = 1 - 4*x^2 - x^3 + 2*x^4 + 4*x^5 + 8*x^6 - 2*x^7 - 5*x^8 - 9*x^9 + ...
%e G.f. = q^17 - 4*q^65 - q^89 + 2*q^113 + 4*q^137 + 8*q^161 - 2*q^185 + ...
%t a[ n_] := SeriesCoefficient[ QPochhammer[ x^2]^4 QPochhammer[ x^3] / QPochhammer[ x^6, x^12], {x, 0, n}];
%o (PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n), polcoeff( eta(x^2 + A)^4 * eta(x^3 + A) * eta(x^12 + A) / eta(x^6 + A), n))};
%Y Cf. A258771.
%K sign
%O 0,3
%A _Michael Somos_, Jun 09 2015
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