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%I #7 Jul 31 2018 21:16:37
%S 1,1,6,12,5,36,60,24,150,228,86,504,732,262,1488,2088,725,3996,5460,
%T 1852,9972,13344,4436,23472,30876,10103,52644,68268,22040,113364,
%U 145224,46336,235734,298800,94378,475488,597108,186926,933672,1162824,361126,1790028
%N Expansion of 3 * a(q^2) * b(q^2) * c(q^2) / (b(q) * c(q)^2) in powers of q where a(), b(), c() are cubic AGM theta functions.
%C Cubic AGM theta functions: a(q) (see A004016), b(q) (A005928), c(q) (A005882).
%H G. C. Greubel, <a href="/A263538/b263538.txt">Table of n, a(n) for n = 0..2500</a>
%F a(n) = A262930(2*n).
%e G.f. = 1 + x + 6*x^2 + 12*x^3 + 5*x^4 + 36*x^5 + 60*x^6 + 24*x^7 + 150*x^8 + ...
%t a:= With[{nmax = 50}, CoefficientList[Series[(QPochhammer[x^2]^3 + 9*x^2*QPochhammer[x^18]^3)*QPochhammer[x^2]^2*QPochhammer[x^6]/ (QPochhammer[x]*QPochhammer[x^3]^5), {x, 0, nmax}], x]]; Table[a[[n]], {n, 1, 50}] (* _G. C. Greubel_, Jul 31 2018 *)
%o (PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( (eta(x^2 + A)^3 + 9 * x^2 * eta(x^18 + A)^3) * eta(x^2 + A)^2 * eta(x^6 + A) / (eta(x + A) * eta(x^3 + A)^5), n))};
%Y Cf. A262930.
%K nonn
%O 0,3
%A _Michael Somos_, Oct 20 2015