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A224825
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Expansion of psi(x) * psi(x^3)^2 in powers of x where psi() is a Ramanujan theta function.
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2
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1, 1, 0, 3, 2, 0, 4, 1, 0, 5, 3, 0, 5, 4, 0, 5, 1, 0, 7, 5, 0, 7, 4, 0, 9, 0, 0, 7, 6, 0, 6, 6, 0, 11, 3, 0, 8, 5, 0, 10, 6, 0, 8, 2, 0, 9, 6, 0, 14, 8, 0, 10, 0, 0, 15, 7, 0, 7, 8, 0, 7, 4, 0, 14, 9, 0, 14, 6, 0, 16, 1, 0, 8, 11, 0, 13, 10, 0, 13, 0, 0, 12
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OFFSET
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0,4
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COMMENTS
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LINKS
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FORMULA
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Expansion of q^(-7/8) * eta(q^2)^2 * eta(q^6)^4 / (eta(q) * eta(q^3)^2) in powers of q.
Euler transform of period 6 sequence [1, -1, 3, -1, 1, -3, ...].
G.f.: (Sum_{k>0} x^(k*(k-1)/2)) * (Sum_{k>0} x^(3 * k*(k-1)/2))^2.
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EXAMPLE
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G.f. = 1 + x + 3*x^3 + 2*x^4 + 4*x^6 + x^7 + 5*x^9 + 3*x^10 + 5*x^12 + 4*x^13 + ...
G.f. = q^7 + q^15 + 3*q^31 + 2*q^39 + 4*q^55 + q^63 + 5*q^79 + 3*q^87 + 5*q^103 + ...
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MATHEMATICA
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a[ n_] := SeriesCoefficient[ EllipticTheta[ 2, 0, q^(1/2)] EllipticTheta[ 2, 0, q^(3/2)]^2 / (8 q^(7/8)), {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^2 + A)^2 * eta(x^6 + A)^4 / (eta(x + A) * eta(x^3 + A)^2), n))};
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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