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A258279
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Expansion of psi(q)^2 * chi(-q^3)^2 in powers of q where psi(), chi() are Ramanujan theta functions.
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5
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1, 2, 1, 0, -2, -2, 0, 0, 1, -4, -4, 0, 0, 4, 0, 0, -2, -2, 4, 0, 2, 0, 0, 0, 0, 6, 2, 0, 0, -2, 0, 0, 1, 0, -4, 0, 4, 4, 0, 0, -4, -2, 0, 0, 0, -8, 0, 0, 0, 2, 3, 0, -4, -2, 0, 0, 0, 0, -4, 0, 0, 4, 0, 0, -2, -4, 0, 0, 2, 0, 0, 0, 4, 4, 2, 0, 0, 0, 0, 0, 2
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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 eta(q^2)^4 * eta(q^3)^2 / (eta(q)^2 * eta(q^6)^2) in powers of q.
Euler transform of period 6 sequence [ 2, -2, 0, -2, 2, -2, ...].
G.f. is a period 1 Fourier series which satisfies f(-1 / (72 t)) = 36 (t/i) g(t) where q = exp(2 Pi i t) and g(t) is the g.f. for A002175.
G.f.: Product_{k>0} (1 - x^(2*k))^2 / (1 - x^k + x^(2*k))^2.
a(18*n) = A004018(n). a(18*n + 3) = a(18*n + 6) = a(18*n + 12) = 0.
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EXAMPLE
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G.f. = 1 + 2*q + q^2 - 2*q^4 - 2*q^5 + q^8 - 4*q^9 - 4*q^10 + 4*q^13 + ...
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MATHEMATICA
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a[ n_] := SeriesCoefficient[ EllipticTheta[ 3, Pi/6, q]^2, {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^2 + A)^2 * eta(x^3 + A) / (eta(x + A) * eta(x^6 + 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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