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A073306
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a(n) = Product_{2i<n} binomial(2*n-2*i-1, 2*i).
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0
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1, 1, 1, 3, 10, 105, 1260, 48510, 2162160, 312161850, 52562109600, 28836887379300, 18539497049673600, 38989721014029185400, 96410946507417622080000, 782067521015701609508820000
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OFFSET
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0,4
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LINKS
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FORMULA
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a(n) ~ A^(3/4) * 2^(n^2/2 - n/2 - 1/48) * exp(n/4 - 1/16) / (Gamma(1/4)^(1/2) * Pi^(n/4 - 1/4) * n^(n/4 + 1/16)) if n is even,
a(n) ~ A^(3/4) * Gamma(1/4)^(1/2) * 2^(n^2/2 - n/2 - 13/48) * exp(n/4 - 1/16) / (Pi^(n/4 + 1/2) * n^(n/4 + 1/16)) if n is odd,
where A is the Glaisher-Kinkelin constant A074962.
(End)
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MATHEMATICA
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Table[Product[Binomial[2n-2i-1, 2i], {i, Floor[(n-1)/2]}], {n, 0, 20}] (* Harvey P. Dale, Nov 29 2011 *)
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PROG
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(PARI) {a(n) = prod( i=0, (n-1)\2, binomial( 2*n - 2*i - 1, 2*i))}
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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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