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A213625
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Expansion of psi(x)^2 * phi(x^2) in powers of x where phi(), psi() are Ramanujan theta functions.
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8
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1, 2, 3, 6, 4, 4, 7, 2, 8, 10, 4, 10, 9, 6, 8, 10, 4, 8, 16, 8, 9, 12, 8, 12, 20, 6, 8, 10, 8, 18, 11, 12, 8, 20, 12, 8, 20, 6, 20, 26, 8, 8, 15, 10, 16, 18, 12, 16, 20, 10, 16, 16, 8, 24, 24, 8, 21, 26, 8, 20, 20, 14, 8, 28, 16, 10, 28, 10, 24, 22, 8, 16, 17
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OFFSET
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0,2
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COMMENTS
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LINKS
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FORMULA
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Expansion of q^(-1/4) * eta(q^2)^2 * eta(q^4)^5 / (eta(q)^2 * eta(q^8)^2) in powers of q.
Euler transform of period 8 sequence [ 2, 0, 2, -5, 2, 0, 2, -3, ...].
G.f. is a period 1 Fourier series which satisfies f(-1 / (32 t)) = 2^(3/2) (t/i)^(3/2) g(t) where q = exp(2 Pi i t) and g() is the g.f. for A116597.
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EXAMPLE
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G.f. = 1 + 2*x + 3*x^2 + 6*x^3 + 4*x^4 + 4*x^5 + 7*x^6 + 2*x^7 + 8*x^8 + 10*x^9 + ...
G.f. = q + 2*q^5 + 3*q^9 + 6*q^13 + 4*q^17 + 4*q^21 + 7*q^25 + 2*q^29 + 8*q^33 + ...
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MATHEMATICA
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a[ n_] := SeriesCoefficient[ EllipticTheta[ 2, 0, x^(1/2)]^2 EllipticTheta[ 3, 0, x^2] / (4 x^(1/4)), {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^4 + A)^5 / (eta(x + A)^2 * eta(x^8 + 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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