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A004425
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Expansion of (Sum x^(n^2), n = -inf .. inf )^(-24).
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4
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1, -48, 1200, -20800, 280752, -3142560, 30338880, -259459200, 2003790000, -14178640368, 92960115360, -569803615680, 3289122824000, -17987650183200, 93669997008000, -466466351287680, 2229627536828592, -10261752523778400
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OFFSET
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0,2
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COMMENTS
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In general, if g.f. = Product_{k>=1} ((1+x^k)/(1-x^k))^m and m>=1, then a(n) ~ exp(Pi*sqrt(m*n)) * m^((m+1)/4) / (2^(3*(m+1)/2) * n^((m+3)/4)) * (1 - (m+3)*(m+1)/(8*Pi*sqrt(m*n))).
If g.f. = Product_{k>=1} ((1+(-x)^k)/(1-(-x)^k))^m and m>=1, then a(n) ~ (-1)^n * exp(Pi*sqrt(m*n)) * m^((m+1)/4) / (2^(3*(m+1)/2) * n^((m+3)/4)) * (1 - (m+3)*(m+1)/(8*Pi*sqrt(m*n))).
(End)
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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 = 24 for this sequence. - Vaclav Kotesovec, Aug 18 2015
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MATHEMATICA
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nmax = 30; CoefficientList[Series[Product[((1 + (-x)^k)/(1 - (-x)^k))^24, {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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