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A320078
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Expansion of Product_{k>0} theta_3(q^(2*k-1)), where theta_3() is the Jacobi theta function.
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10
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1, 2, 0, 2, 6, 2, 4, 6, 8, 16, 8, 14, 26, 26, 24, 30, 58, 50, 60, 78, 90, 118, 104, 138, 192, 224, 204, 268, 366, 354, 412, 474, 596, 694, 724, 818, 1052, 1162, 1176, 1470, 1756, 1918, 2052, 2434, 2814, 3168, 3396, 3806, 4674, 5124, 5396, 6250, 7374, 7898, 8732
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OFFSET
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0,2
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LINKS
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FORMULA
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Expansion of Product_{k>0} eta(q^(2*(2*k-1)))^5 / (eta(q^(2*k-1))*eta(q^(4*(2*k-1))))^2.
a(n) ~ (log(2))^(1/4) * exp(Pi*sqrt(n*log(2)/2)) / (4*n^(3/4)). - Vaclav Kotesovec, Oct 07 2018
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MATHEMATICA
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nmax = 60; CoefficientList[Series[Product[EllipticTheta[3, 0, x^(2*k-1)], {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Oct 05 2018 *)
nmax = 60; CoefficientList[Series[Product[(1 - x^((2*k-1)*j))*(1 + x^((2*k-1)*j))^3/(1 + x^(2*j*(2*k-1)))^2, {k, 1, nmax}, {j, 1, Floor[nmax/k] + 1}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Oct 06 2018 *)
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PROG
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(PARI) q='q+O('q^80); Vec(prod(k=1, 50, eta(q^(2*(2*k-1)))^5/( eta(q^(2*k-1))* eta(q^(4*(2*k-1))))^2 ) ) \\ G. C. Greubel, Oct 29 2018
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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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