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A230256
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Expansion of f(-x) * psi(x^2) * phi(x^3) / f(-x^3)^3 in powers of x where phi(), psi(), f() are Ramanujan theta functions.
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6
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1, -1, 0, 4, -6, 1, 11, -19, 4, 31, -50, 11, 77, -122, 28, 173, -273, 62, 370, -573, 130, 751, -1149, 261, 1461, -2214, 498, 2750, -4125, 923, 5022, -7472, 1663, 8936, -13202, 2919, 15551, -22817, 5019, 26521, -38681, 8467, 44417, -64438, 14035, 73197
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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^(1/12) * eta(q) * eta(q^4)^2 * eta(q^6)^5 / (eta(q^2) * eta(q^3)^5 * eta(q^12)^2) in powers of q.
Euler transform of period 12 sequence [ -1, 0, 4, -2, -1, 0, -1, -2, 4, 0, -1, 0, ...].
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EXAMPLE
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G.f. = 1 - x + 4*x^3 - 6*x^4 + x^5 + 11*x^6 - 19*x^7 + 4*x^8 + 31*x^9 + ...
G.f. = q^-1 - q^11 + 4*q^35 - 6*q^47 + q^59 + 11*q^71 - 19*q^83 + 4*q^95 + ...
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MATHEMATICA
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a[ n_] := SeriesCoefficient[ EllipticTheta[ 2, 0, x] EllipticTheta[ 3, 0, x^3] QPochhammer[ x] / (2 x^(1/4) QPochhammer[ x^3]^3), {x, 0, n}]; (* Michael Somos, Jan 29 2015 *)
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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) * eta(x^4 + A)^2 * eta(x^6 + A)^5 / (eta(x^2 + A) * eta(x^3 + A)^5 * eta(x^12 + A)^2), 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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