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%I #9 Mar 12 2021 22:24:48
%S 1,3,9,22,50,105,208,395,722,1280,2210,3728,6163,10006,15986,25169,
%T 39104,60022,91106,136870,203664,300368,439321,637568,918530,1314214,
%U 1868153,2639276,3706994,5177868,7194304,9945872,13683986,18740880,25554084,34697883
%N Expansion of phi(-x^6)^2 / (chi(x) * phi(-x)^2) in powers of x where phi(), 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="/A260545/b260545.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^(-1/24) * eta(q^4) * eta(q^6)^4 / (eta(q)^3 * eta(q^12)^2) in powers of q.
%F Euler transform of period 12 sequence [ 3, 3, 3, 2, 3, -1, 3, 2, 3, 3, 3, 0, ...].
%F a(n) = A001935(3*n).
%e G.f. = 1 + 3*x + 9*x^2 + 22*x^3 + 50*x^4 + 105*x^5 + 208*x^6 + 395*x^7 + ...
%e G.f. = q + 3*q^25 + 9*q^49 + 22*q^73 + 50*q^97 + 105*q^121 + 208*q^145 + ...
%t a[ n_] := SeriesCoefficient[ EllipticTheta[ 4, 0, x^6]^2 QPochhammer[ x^4] / QPochhammer[ x]^3, {x, 0, n}];
%t a[ n_] := SeriesCoefficient[ QPochhammer[ x, -x] EllipticTheta[ 4, 0, x^6]^2 / EllipticTheta[ 4, 0, x]^2, {x, 0, n}];
%o (PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^4 + A) * eta(x^6 + A)^4 / (eta(x + A)^3 * eta(x^12 + A)^2), n))};
%Y Cf. A001935.
%K nonn
%O 0,2
%A _Michael Somos_, Jul 28 2015
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