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A262930
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Expansion of (psi(-q) / f(q^3))^2 in powers of q where psi(), f() are Ramanujan theta functions.
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6
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1, -2, 1, -4, 6, -2, 12, -16, 5, -28, 36, -12, 60, -76, 24, -120, 150, -46, 228, -280, 86, -416, 504, -152, 732, -878, 262, -1252, 1488, -442, 2088, -2464, 725, -3408, 3996, -1168, 5460, -6364, 1852, -8600, 9972, -2886, 13344, -15400, 4436, -20424, 23472
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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 ( eta(q) * eta(q^3) * eta(q^4) * eta(q^12) / ( eta(q^2) * eta(q^6)^3 ))^2 in powers of q.
Euler transform of period 12 sequence [ -2, 0, -4, -2, -2, 4, -2, -2, -4, 0, -2, 0, ...].
G.f. is a period 1 Fourier series which satisfies f(-1 / (36 t)) = 3 g(t) where q = exp(2 Pi i t) and g() is the g.f. of A261369.
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EXAMPLE
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G.f. = 1 - 2*x + x^2 - 4*x^3 + 6*x^4 - 2*x^5 + 12*x^6 - 16*x^7 + 5*x^8 + ...
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MATHEMATICA
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a[ n_] := SeriesCoefficient[ (1/2) q^(-1/4) (EllipticTheta[ 2, Pi/4, q^(1/2)] / QPochhammer[ -q^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^3 + A) * eta(x^4 + A) * eta(x^12 + A) / ( eta(x^2 + A) * eta(x^6 + 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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