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A226350
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Expansion of psi(x) * psi(-x^3) in powers of x where psi() is a Ramanujan theta function.
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1
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1, 1, 0, 0, -1, 0, 0, 0, 0, -2, 0, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -1, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 2, -1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -2, 0
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OFFSET
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0,10
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COMMENTS
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LINKS
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FORMULA
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Expansion of q^(-1/2) * eta(q^2)^2 * eta(q^3) * eta(q^12) / (eta(q) * eta(q^6)) in powers of q.
Euler transform of period 12 sequence [ 1, -1, 0, -1, 1, -1, 1, -1, 0, -1, 1, -2, ...].
a(3*n + 2) = a(4*n + 2) = a(4*n + 3) = 0.
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EXAMPLE
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1 + x - x^4 - 2*x^9 - x^12 - x^13 + 2*x^21 - x^24 + 2*x^28 + 2*x^33 + ...
q + q^3 - q^9 - 2*q^19 - q^25 - q^27 + 2*q^43 - q^49 + 2*q^57 + 2*q^67 + ...
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MATHEMATICA
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a[ n_] := SeriesCoefficient[ EllipticTheta[ 2, 0, q] EllipticTheta[ 2, Pi/4, q^3]/8^(1/2), {q, 0, 2 n + 1}]
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PROG
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(PARI) {a(n) = local(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^2 + A)^2 * eta(x^3 + A) * eta(x^12 + A) / (eta(x + A) * eta(x^6 + A)), 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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