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%I #15 Dec 17 2023 18:41:32
%S 1,2,1,2,2,0,3,2,0,2,2,2,1,2,0,2,4,0,2,0,1,4,2,2,6,4,4,6,2,8,5,4,4,4,
%T 6,2,8,2,6,10,0,4,3,4,8,6,5,6,7,4,6,8,7,4,8,6,5,8,3,10,6,8,8,0,4,8,9,
%U 6,6,12,8,8,11,8,10,8,9,4,14,12,10,12,8,8
%N Expansion of (q^3 * psi(q) * psi(q^23))^2 in powers of q where psi() 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="/A253183/b253183.txt">Table of n, a(n) for n = 6..2500</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) * eta(q^46))^4 / (eta(q) * eta(q^23))^2 in powers of q.
%F Euler transform of a period 46 sequence.
%F G.f.: x^6 * (Sum_{k>0} x^(k * (k-1) / 2))^2 * (Sum_{k>0} x^(23 * k * (k-1) / 2))^2.
%F G.f.: x^6 * (Product_{k>0} (1 + x^k) * (1 - x^(2*k)) * (1 + x^(23*k)) * (1 - x^(46*k)))^2.
%F Convolution square of A033782.
%e G.f. = q^6 + 2*q^7 + q^8 + 2*q^9 + 2*q^10 + 3*q^12 + 2*q^13 + 2*q^15 + ...
%t a[ n_] := SeriesCoefficient[ q^6 (QPochhammer[ q^2] QPochhammer[ q^46])^4 / (QPochhammer[ q] QPochhammer[ q^23])^2, {q, 0 ,n}];
%o (PARI) {a(n) = my(A); if( n<6, 0, n -= 6; A = x * O(x^n); polcoeff( (eta(x^2 + A) * eta(x^46 + A))^4 / (eta(x + A) * eta(x^23 + A))^2, n))};
%Y Cf. A033782.
%K nonn
%O 6,2
%A _Michael Somos_, Mar 23 2015
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