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G. C. Greubel, <a href="/A263538/b263538.txt">Table of n, a(n) for n = 0..2500</a>

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 *)

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allocated for Michael SomosExpansion 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.

1, 1, 6, 12, 5, 36, 60, 24, 150, 228, 86, 504, 732, 262, 1488, 2088, 725, 3996, 5460, 1852, 9972, 13344, 4436, 23472, 30876, 10103, 52644, 68268, 22040, 113364, 145224, 46336, 235734, 298800, 94378, 475488, 597108, 186926, 933672, 1162824, 361126, 1790028

0,3

Cubic AGM theta functions: a(q) (see A004016), b(q) (A005928), c(q) (A005882).

a(n) = A262930(2*n).

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 + ...

(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))};

Cf. A262930.

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Michael Somos, Oct 20 2015

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allocated for Michael Somos

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