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A231961 Expansion of b(q)^3 - 3*c(q)^3 in powers of q where b(), c() are cubic AGM theta functions.

%I A231961 #12 Aug 08 2018 22:52:34
%S A231961 1,-90,-216,-738,-1170,-1728,-2160,-4500,-3672,-6570,-6480,-8640,
%T A231961 -9594,-15300,-10800,-17280,-18450,-20736,-19656,-32580,-22464,-36900,
%U A231961 -32400,-38016,-36720,-54090,-36720,-59058,-58500,-60480,-53136,-86580,-58968,-86400,-77760
%N A231961 Expansion of b(q)^3 - 3*c(q)^3 in powers of q where b(), c() are cubic AGM theta functions.
%C A231961 Cubic AGM theta functions: a(q) (see A004016), b(q) (A005928), c(q) (A005882).
%H A231961 G. C. Greubel, <a href="/A231961/b231961.txt">Table of n, a(n) for n = 0..2500</a>
%F A231961 Expansion of (eta(q)^3 / eta(q^3))^3 - 81 * (eta(q^3)^3 / eta(q))^3 in powers of q.
%F A231961 G.f. is a period 1 Fourier series which satisfies f(-1 / (3 t)) = - 3^(5/2) (t/i)^3 g(t) where q = exp(2 Pi i t) and g() is the g.f. for A231962.
%F A231961 a(n) = A231948(3*n) = A231962(3*n).
%e A231961 G.f. = 1 - 90*q - 216*q^2 - 738*q^3 - 1170*q^4 - 1728*q^5 - 2160*q^6 + ...
%t A231961 eta[q_]:= q^(1/24)*QPochhammer[q]; CoefficientList[Series[(eta[q]^3/ eta[q^3])^3 - 81*(eta[q^3]^3/eta[q])^3, {q, 0, 50}], q] (* _G. C. Greubel_, Aug 08 2018 *)
%o A231961 (PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( (eta(x + A)^3 / eta(x^3 + A))^3 - 81 * x * (eta(x^3 + A)^3 / eta(x + A))^3, n))};
%Y A231961 Cf. A231948, A231962.
%K A231961 sign
%O A231961 0,2
%A A231961 _Michael Somos_, Nov 15 2013