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A296590
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a(n) = Product_{k=0..n} binomial(2*n - k, k).
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4
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1, 1, 3, 30, 1050, 132300, 61122600, 104886381600, 674943865596000, 16407885372638760000, 1515727634953623371280000, 534621388490302221024396480000, 722849817707190846398223943885440000, 3759035907022704558524683975387453632000000
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OFFSET
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0,3
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COMMENTS
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LINKS
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FORMULA
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a(n) = A^(3/2) * 2^(n^2 - 1/24) * BarnesG(n + 3/2) / (exp(1/8) * Pi^(n/2 + 1/4) * BarnesG(n + 2)), where A is the Glaisher-Kinkelin constant A074962.
a(n) ~ A^(3/2) * exp(n/2 - 1/8) * 2^(n^2 - 7/24) / (Pi^((n+1)/2) * n^(n/2 + 3/8)), where A is the Glaisher-Kinkelin constant A074962.
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MAPLE
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mul( binomial(2*n-k, k), k=0..n) ;
end proc:
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MATHEMATICA
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Table[Product[Binomial[2*n-k, k], {k, 0, n}], {n, 0, 15}]
Table[Glaisher^(3/2) * 2^(n^2 - 1/24) * BarnesG[n + 3/2] / (E^(1/8) * Pi^(n/2 + 1/4) * BarnesG[n + 2]), {n, 0, 15}]
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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