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A261992
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Expansion of psi(x) * f(-x^18)^3 / (phi(-x^3) * f(-x^3)^3) in powers of x where phi(), psi(), f() are Ramanujan theta functions.
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2
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1, 1, 0, 6, 5, 0, 25, 19, 0, 84, 61, 0, 248, 174, 0, 666, 455, 0, 1662, 1112, 0, 3912, 2573, 0, 8774, 5689, 0, 18894, 12102, 0, 39289, 24900, 0, 79248, 49759, 0, 155612, 96902, 0, 298338, 184408, 0, 559812, 343722, 0, 1030224, 628717, 0, 1862647, 1130418, 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^-2 * eta(q^2)^2 * eta(q^6) * eta(q^18)^3 / (eta(q) * eta(q^3)^5) in powers of q.
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EXAMPLE
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G.f. = 1 + x + 6*x^3 + 5*x^4 + 25*x^6 + 19*x^7 + 84*x^9 + 61*x^10 + ...
G.f. = q^2 + q^3 + 6*q^5 + 5*q^6 + 25*q^8 + 19*q^9 + 84*q^11 + 61*q^12 + ...
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MATHEMATICA
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a[ n_] := SeriesCoefficient[ (1/2) x^(-1/8) EllipticTheta[ 2, 0, x^(1/2)] QPochhammer[ x^18]^3 / (EllipticTheta[ 4, 0, x^3] QPochhammer[ x^3]^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^2 + A)^2 * eta(x^6 + A) * eta(x^18 + A)^3 / (eta(x + A) * eta(x^3 + A)^5), 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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