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A298932
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Expansion of f(-x^3)^3 * phi(-x^12) / (f(-x) * chi(-x^4)) in powers of x where phi(), chi(), f() are Ramanujan theta functions.
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3
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1, 1, 2, 0, 3, 2, 4, 0, 4, 4, 6, 0, 5, 3, 6, 0, 6, 4, 4, 0, 8, 4, 6, 0, 9, 6, 6, 0, 6, 6, 12, 0, 8, 4, 12, 0, 8, 7, 8, 0, 9, 6, 8, 0, 12, 8, 6, 0, 8, 6, 14, 0, 12, 6, 12, 0, 8, 8, 12, 0, 13, 6, 12, 0, 18, 10, 8, 0, 8, 12, 12, 0, 16, 7, 14, 0, 12, 8, 12, 0, 16
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OFFSET
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0,3
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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^3)^3 * eta(q^8) * eta(q^12)^2 / (eta(q) * eta(q^4) * eta(q^24)) in powers of q.
Euler transform of period 24 sequence [1, 1, -2, 2, 1, -2, 1, 1, -2, 1, 1, -3, 1, 1, -2, 1, 1, -2, 1, 2, -2, 1, 1, -3, ...].
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EXAMPLE
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G.f. = 1 + x + 2*x^2 + 3*x^4 + 2*x^5 + 4*x^6 + 4*x^8 + 4*x^9 + ...
G.f. = q + q^3 + 2*q^5 + 3*q^9 + 2*q^11 + 4*q^13 + 4*q^17 + 4*q^19 + ...
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MATHEMATICA
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a[ n_] := SeriesCoefficient[ QPochhammer[ x^3]^3 QPochhammer[ -x^4, x^4] EllipticTheta[ 4, 0, x^12] / QPochhammer[ x], {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^3 + A)^3 * eta(x^8 + A) * eta(x^12 + A)^2 / (eta(x + A) * eta(x^4 + A) * eta(x^24 + 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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