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A261877
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Expansion of psi(x^4) / phi(-x^3) in powers of x where phi(), psi() are Ramanujan theta functions.
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3
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1, 0, 0, 2, 1, 0, 4, 2, 0, 8, 4, 0, 15, 8, 0, 26, 14, 0, 44, 24, 0, 72, 40, 0, 115, 64, 0, 180, 100, 0, 276, 154, 0, 416, 232, 0, 618, 344, 0, 906, 505, 0, 1312, 730, 0, 1880, 1044, 0, 2666, 1480, 0, 3746, 2076, 0, 5220, 2888, 0, 7216, 3988, 0, 9903, 5464, 0
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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^(-1/2) * eta(q^6) * eta(q^8)^2 / (eta(q^3)^2 * eta(q^4)) in powers of q.
Euler transform of period 24 sequence [ 0, 0, 2, 1, 0, 1, 0, -1, 2, 0, 0, 2, 0, 0, 2, -1, 0, 1, 0, 1, 2, 0, 0, 0, ...].
2 * a(n) = A143068(2*n + 1). a(3*n + 2) = 0.
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EXAMPLE
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G.f. = 1 + 2*x^3 + x^4 + 4*x^6 + 2*x^7 + 8*x^9 + 4*x^10 + 15*x^12 + ...
G.f. = q + 2*q^7 + q^9 + 4*q^13 + 2*q^15 + 8*q^19 + 4*q^21 + 15*q^25 + ...
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MATHEMATICA
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a[ n_] := SeriesCoefficient[ 1/2 (x^2)^(-1/4) EllipticTheta[ 2, 0, x^2] / EllipticTheta[ 4, 0, x^3], {x, 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^6 + A) * eta(x^8 + A)^2 / (eta(x^3 + A)^2 * eta(x^4 + A)), 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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