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A268505
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a(n) = Product_{k=0..n} (4*k)!.
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13
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1, 24, 967680, 463520268288000, 9698137182219213471744000000, 23594617426193665303453830729600860160000000000, 14639242671589099207353038379393488170313478620292159897600000000000000
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OFFSET
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0,2
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COMMENTS
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LINKS
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FORMULA
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a(n) ~ Gamma(1/4)^(1/2) * 2^(5/6 + 11*n/2 + 4*n^2) * exp(1/48 - 5*n/2 - 3*n^2) * n^(29/48 + 5*n/2 + 2*n^2) * Pi^(1/4 + n/2) / A^(1/4), where A = A074962 is the Glaisher-Kinkelin constant.
a(n) = A^(15/4) * sqrt(Gamma(1/4)) * exp(-5/16) * 2^(4*n^2 + 7*n/2 - 5/12) * BarnesG(n + 5/4) * BarnesG(n + 3/2) * BarnesG(n + 7/4) * BarnesG(n+2) / Pi^(3*n/2 + 1). - Vaclav Kotesovec, Apr 23 2024
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MATHEMATICA
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Table[Product[(4*k)!, {k, 0, n}], {n, 0, 8}]
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PROG
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CROSSREFS
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KEYWORD
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nonn,changed
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AUTHOR
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STATUS
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approved
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