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A246838
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Expansion of f(-x^2) * f(-x^12)^2 / f(x^1, x^5) in powers of x where f() is Ramanujan theta function.
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4
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1, -1, 0, 0, -1, 0, 1, -1, 0, 2, -1, 0, 0, 0, 0, 2, -1, 0, 1, -1, 0, 0, -2, 0, 0, -1, 0, 2, 0, 0, 0, -1, 0, 0, -1, 0, 3, -1, 0, 0, -1, 0, 2, -1, 0, 2, 0, 0, 0, -1, 0, 0, -1, 0, 2, -1, 0, 0, 0, 0, 1, -2, 0, 0, -2, 0, 0, -1, 0, 2, -1, 0, 2, 0, 0, 0, -1, 0, 0, 0
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OFFSET
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0,10
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COMMENTS
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LINKS
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FORMULA
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Expansion of q^(-3/4) * eta(q) * eta(q^4) * eta(q^6) * eta(q^12) / (eta(q^2) * eta(q^3)) in powers of q.
Euler transform of period 12 sequence [ -1, 0, 0, -1, -1, 0, -1, -1, 0, 0, -1, -2, ...].
G.f. is a period 1 Fourier series which satisfies f(-1 / (144 t)) = 27^(1/2) (t/i) g(t) where q = exp(2 Pi i t) and g() is the g.f. for A246752.
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EXAMPLE
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G.f. = 1 - x - x^4 + x^6 - x^7 + 2*x^9 - x^10 + 2*x^15 - x^16 + x^18
+ ...
G.f. = q^3 - q^7 - q^19 + q^27 - q^31 + 2*q^39 - q^43 + 2*q^63 - q^67 + ...
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MATHEMATICA
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a[ n_] := SeriesCoefficient[ x^(1/4) EllipticTheta[ 2, Pi/4, x^(1/2)] QPochhammer[ x^12]^2 / EllipticTheta[ 2, Pi/4, x^(3/2)], {x, 0, n}]; (* Michael Somos, Aug 27 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) * eta(x^6 + A) * eta(x^12 + A) / (eta(x^2 + A) * eta(x^3 + A)), 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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