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%I #12 Mar 12 2021 22:24:48
%S 1,12,80,400,1664,6056,19904,60320,171008,458428,1171552,2872368,
%T 6790656,15544136,34568576,74901984,158507008,328277848,666568592,
%U 1329014992,2605464320,5028397952,9563654976,17942323424,33232441344,60814373780,110029864416
%N Expansion of (phi(-x^2) * phi(-x^4)^2 / phi(-x)^3)^2 in powers of x where phi() is a Ramanujan theta function.
%C Ramanujan theta functions: f(q) (see A121373), phi(q) (A000122), psi(q) (A010054), chi(q) (A000700).
%H G. C. Greubel, <a href="/A258591/b258591.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 (eta(q^2)^5 * eta(q^4)^3 / (eta(q)^6 * eta(q^8)^2))^2 in powers of q.
%F Euler transform of period 8 sequence [ 12, 2, 12, -4, 12, 2, 12, 0, ...].
%F a(n) = A260186(2*n).
%e G.f. = 1 + 12*x + 80*x^2 + 400*x^3 + 1664*x^4 + 6056*x^5 + 19904*x^6 + ...
%t a[ n_] := SeriesCoefficient[ EllipticTheta[ 4, 0, x^2]^2 EllipticTheta[ 4, 0, x^4]^4 / EllipticTheta[ 4, 0, x]^6, {x, 0, n}];
%o (PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( (eta(x^2 + A)^5 * eta(x^4 + A)^3 / (eta(x + A)^6 * eta(x^8 + A)^2))^2, n))};
%Y Cf. A260186.
%K nonn
%O 0,2
%A _Michael Somos_, Nov 06 2015
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