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A224822
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Expansion of phi(-q) * phi(-q^3)^2 in powers of q where phi() is a Ramanujan theta function.
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3
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1, -2, 0, -4, 10, 0, 4, -16, 0, -2, 8, 0, 12, -8, 0, -16, 26, 0, 0, -24, 0, -8, 8, 0, 20, -10, 0, -4, 32, 0, 8, -48, 0, -8, 16, 0, 10, -8, 0, -32, 40, 0, 8, -24, 0, 0, 16, 0, 28, -18, 0, -24, 40, 0, 4, -64, 0, -8, 8, 0, 32, -24, 0, -16, 58, 0, 16, -24, 0, -16
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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)^2 * eta(q^3)^4 / (eta(q^2) * eta(q^6)^2) in powers of q.
Euler transform of period 6 sequence [-2, -1, -6, -1, -2, -3, ...].
G.f.: (Sum_{k in Z} (-1)^k * x^k^2) * (Sum_{k in Z} (-1)^k * x^(3*k^2))^2.
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EXAMPLE
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G.f. = 1 - 2*q - 4*q^3 + 10*q^4 + 4*q^6 - 16*q^7 - 2*q^9 + 8*q^10 + 12*q^12 +
...
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MATHEMATICA
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a[ n_] := SeriesCoefficient[ EllipticTheta[ 4, 0, q] EllipticTheta[ 4, 0, 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)^2 * eta(x^3 + A)^4 / (eta(x^2 + A) * eta(x^6 + A)^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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