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A261576
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Expansion of 3 * b(q^2) * c(q^2) / c(q)^2 in powers of q where b(), c() are cubic AGM theta functions.
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2
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1, -2, -3, 12, -10, -18, 60, -48, -75, 228, -172, -252, 732, -524, -744, 2088, -1450, -1998, 5460, -3704, -4986, 13344, -8872, -11736, 30876, -20206, -26322, 68268, -44080, -56682, 145224, -92672, -117867, 298800, -188756, -237744, 597108, -373852, -466836
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OFFSET
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0,2
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COMMENTS
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LINKS
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FORMULA
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Expansion of f(-q^2)^4 / (f(-q^3)^2 * f(q, q^2)^2) in powers of q where f(,) is Ramanujan's general theta function.
Expansion of (eta(q) * eta(q^2) * eta(q^6) / eta(q^3)^3)^2 in powers of q.
Euler transform of period 6 sequence [ -2, -4, 4, -4, -2, 0, ...].
G.f. is a period 1 Fourier series which satisfies f(-1 / (18 t)) = 9/4 g(t) where q = exp(2 Pi i t) and g() is the g.f. of A258099.
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EXAMPLE
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G.f. = 1 - 2*x - 3*x^2 + 12*x^3 - 10*x^4 - 18*x^5 + 60*x^6 - 48*x^7 + ...
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MATHEMATICA
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a[ n_] := SeriesCoefficient[ (QPochhammer[ q] QPochhammer[ q^2] QPochhammer[ q^6] / QPochhammer[ q^3]^3)^2, {q, 0, n}];
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PROG
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(PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( (eta(x + A) * eta(x^2 + A) * eta(x^6 + A) / eta(x^3 + A)^3)^2, n))};
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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