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A257398
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Expansion of phi(-x^6)^2 / chi(-x) in powers of x where phi(), chi() are Ramanujan theta functions.
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6
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1, 1, 1, 2, 2, 3, 0, 1, 2, 0, 2, 0, 3, 2, 2, 3, 0, 2, 2, 2, 0, 0, 1, 0, 2, 2, 1, 4, 2, 4, 0, 0, 2, 0, 4, 1, 0, 0, 4, 2, 1, 0, 2, 2, 0, 0, 0, 2, 2, 4, 2, 1, 2, 4, 2, 2, 0, 1, 0, 0, 4, 0, 2, 4, 0, 0, 0, 2, 0, 2, 3, 0, 0, 2, 2, 2, 2, 3, 2, 0, 4, 0, 4, 2, 2, 0, 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 phi(x^3) * f(x, x^2) in powers of x where phi() is a Ramanujan theta function and f(, ) is Ramanujan's general theta function.
Expansion of q^(-1/24) * eta(q^2) * eta(q^6)^4 / (eta(q) * eta(q^12)^2) in powers of q.
Euler transform of period 12 sequence [1, 0, 1, 0, 1, -4, 1, 0, 1, 0, 1, -2, ...].
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EXAMPLE
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G.f. = 1 + x + x^2 + 2*x^3 + 2*x^4 + 3*x^5 + x^7 + 2*x^8 + 2*x^10 + ...
G.f. = q + q^25 + q^49 + 2*q^73 + 2*q^97 + 3*q^121 + q^169 + 2*q^193 + ...
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MATHEMATICA
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a[ n_] := SeriesCoefficient[ QPochhammer[ -x, x] EllipticTheta[ 4, 0, x^6] ^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^2 + A) * eta(x^6 + A)^4 / (eta(x + A) * eta(x^12 + A)^2), 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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