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A263452
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Expansion of f(-q^3)^3 * psi(q^12) / f(-q) in powers of q where ps(), f() are Ramanujan theta functions.
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3
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1, 1, 2, 0, 2, 1, 2, 0, 1, 2, 2, 0, 3, 1, 4, 0, 5, 3, 2, 0, 3, 3, 4, 0, 4, 2, 4, 0, 3, 2, 4, 0, 4, 2, 4, 0, 5, 5, 4, 0, 3, 3, 8, 0, 7, 3, 6, 0, 4, 4, 4, 0, 6, 4, 4, 0, 9, 3, 6, 0, 4, 4, 4, 0, 4, 3, 8, 0, 5, 5, 6, 0, 9, 3, 4, 0, 7, 6, 6, 0, 7, 6, 10, 0, 6, 3
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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^(-11/6) * eta(q^3)^3 * eta(q^24)^2 / (eta(q) * eta(q^12)) in powers of q.
Euler transform of period 24 sequence [ 1, 1, -2, 1, 1, -2, 1, 1, -2, 1, 1, -1, 1, 1, -2, 1, 1, -2, 1, 1, -2, 1, 1, -3, ...].
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EXAMPLE
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G.f. = 1 + x + 2*x^2 + 2*x^4 + x^5 + 2*x^6 + x^8 + 2*x^9 + 2*x^10 + ...
G.f. = q^11 + q^17 + 2*q^23 + 2*q^35 + q^41 + 2*q^47 + q^59 + 2*q^65 + ...
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MATHEMATICA
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a[ n_] := SeriesCoefficient[ QPochhammer[ q^3]^3 EllipticTheta[ 2, 0, q^6] / ( 2 q^(3/2) QPochhammer[ q]), {q, 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^24 + A)^2 / (eta(x + A) * eta(x^12 + 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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