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%I #17 Mar 12 2021 22:24:46
%S 1,1,2,1,3,3,2,2,2,5,3,3,4,4,3,4,3,5,3,6,6,3,4,5,5,7,5,4,4,4,8,3,6,7,
%T 9,7,5,4,3,9,7,4,7,5,10,5,8,8,4,7,9,6,8,7,8,10,5,6,5,9,10,7,8,6,7,10,
%U 7,12,6,10,7,5,12,6,12,14,6,6,5,11,6,8,10
%N Expansion of x^(-1/3) * psi(x^3) * c(x) / 3 in powers of x where psi() is a Ramanujan theta function and c() is a cubic AGM 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="/A212907/b212907.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^3)^2 * eta(q^6)^2 / eta(q) in powers of q.
%F Euler transform of period 6 sequence [ 1, 1, -1, 1, 1, -3, ...].
%F G.f.: Product_{k>0} (1 - x^(3*k))^2 * (1 - x^(6*k))^2 / (1 - x^k).
%e 1 + x + 2*x^2 + x^3 + 3*x^4 + 3*x^5 + 2*x^6 + 2*x^7 + 2*x^8 + 5*x^9 + ...
%e q^17 + q^41 + 2*q^65 + q^89 + 3*q^113 + 3*q^137 + 2*q^161 + 2*q^185 + ...
%t QP := QPochhammer; a[n_]:= SeriesCoefficient[(QP[q^3]*QP[q^6])^2/QP[q], {q, 0, n}]; Table[a[n], {n,0,50}] (* _G. C. Greubel_, Jan 07 2018 *)
%o (PARI) {a(n) = local(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^3 + A)^2 * eta(x^6 + A)^2 / eta(x + A), n))}
%K nonn
%O 0,3
%A _Michael Somos_, Jun 16 2012
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