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A261251
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Expansion of f(-x, -x) * f(-x^3, -x^15) / f(-x^6, -x^12)^2 in powers of x where f(,) is Ramanujan's general theta function.
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2
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1, -2, 0, -1, 4, 0, 2, -6, 0, -4, 8, 0, 7, -14, 0, -10, 24, 0, 14, -34, 0, -22, 48, 0, 33, -72, 0, -45, 104, 0, 62, -142, 0, -88, 192, 0, 122, -266, 0, -163, 364, 0, 216, -480, 0, -290, 632, 0, 386, -840, 0, -502, 1104, 0, 650, -1426, 0, -846, 1832, 0, 1093
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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 phi(-x) * psi(x^9) / (f(-x^6) * psi(x^3)) in powers of x where phi(), psi(), f() are Ramanujan theta functions.
Expansion of q^(-1/2) * eta(q)^2 * eta(q^3) * eta(q^18)^2 / (eta(q^2) * eta(q^6)^3 * eta(q^9)) in powers of q.
Euler transform of period 18 sequence [ -2, -1, -3, -1, -2, 1, -2, -1, -2, -1, -2, 1, -2, -1, -3, -1, -2, 0, ...].
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EXAMPLE
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G.f. = 1 - 2*x - x^3 + 4*x^4 + 2*x^6 - 6*x^7 - 4*x^9 + 8*x^10 + ...
G.f. = q - 2*q^3 - q^7 + 4*q^9 + 2*q^13 - 6*q^15 - 4*q^19 + 8*q^21 + ...
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MATHEMATICA
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a[ n_] := SeriesCoefficient[ x^(-3/4) EllipticTheta[ 4, 0, x] EllipticTheta[ 2, 0, x^(9/2)] / (QPochhammer[ x^6] EllipticTheta[ 2, 0, x^(3/2)]), {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 + A)^2 * eta(x^3 + A) * eta(x^18 + A)^2 / (eta(x^2 + A) * eta(x^6 + A)^3 * eta(x^9 + 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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