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A004414
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Expansion of (Sum_{n=-inf..inf} x^(n^2))^(-13).
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1
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1, -26, 364, -3640, 29094, -197288, 1177176, -6333184, 31258604, -143374530, 617193304, -2513060264, 9739727816, -36115518376, 128680223152, -442158402816, 1469734751654, -4738671343952, 14853923411652
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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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a(n) ~ (-1)^n * exp(Pi*sqrt(m*n)) * m^((m+1)/4) / (2^(3*(m+1)/2) * n^((m+3)/4)), set m = 13 for this sequence. - Vaclav Kotesovec, Aug 18 2015
G.f.: 1/theta_3(x)^13, where theta_3() is the Jacobi theta function.
G.f.: Product_{k>=1} 1/((1 - x^(2*k))*(1 + x^(2*k-1))^2)^13. (End)
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MATHEMATICA
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nmax = 30; CoefficientList[Series[Product[((1 + (-x)^k)/(1 - (-x)^k))^13, {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Aug 18 2015 *)
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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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