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A260448
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Denominators in the asymptotic expansion of the Barnes G-function.
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2
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1, 12, 1440, 51840, 87091200, 1045094400, 376233984000, 902961561600, 166867296583680000, 18021668031037440000, 140569010642092032000000, 1686828127705104384000000, 8501613763633726095360000000, 102019365163604713144320000000, 208119504933753614814412800000000
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OFFSET
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0,2
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COMMENTS
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10^(2m)|a(n) where 5m <= n <= 5m+4, m>=0. Example: for m=4, 20<= n <= 24, the values of a(20) to a(24) are divisible by 10^(10). - G. C. Greubel, Dec 15 2015
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LINKS
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FORMULA
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G(x) ~ exp^(-3*x^2/4 + x + zeta'(-1)) * x^(x^2/2 - x + 5/12) * (2*Pi)^((x-1)/2) * (1 + (-1/12)/x + (-1/1440)/x^2 + (157/51840)/x^3 + (65911/87091200)/x^4 + ...).
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MATHEMATICA
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Denominator[Exp[Series[LogBarnesG[x] - 1/12 - x + 3 x^2/4 + Log[Glaisher] + Log[2 Pi]/2 - x Log[2 Pi]/2 - 5 Log[x]/12 + x Log[x] - x^2 Log[x]/2, {x, Infinity, 20}]][[3]]]
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CROSSREFS
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KEYWORD
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nonn,frac
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AUTHOR
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STATUS
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approved
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