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A057863
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Prod(k=0,n,(2k+1)!!)
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7
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1, 1, 3, 45, 4725, 4465125, 46414974375, 6272287562165625, 12714083695698776015625, 438120013555654794702228515625, 286849911214281324754704976473779296875
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| a(n) is the coefficient of the closed form for BarnesG[(2n-1)/2].
a(n) is the hook product corresponding to the partition (n,n-1,...,2,1). a(n)=(n(n+1)/2)!/A005118(n+1). - Emeric Deutsch (deutsch(AT)duke.poly.edu), May 21 2004
Hankel transform of A185998. - Paul Barry, 8 Feb 2011.
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LINKS
| Eric Weisstein's World of Mathematics, Barnes G-Function
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FORMULA
| a(n)=Product{k=0..n, (2k+1)^(n-k)}.
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MATHEMATICA
| a[n_] := Product[2^i Gamma[1/2+i]/Sqrt[Pi], {i, n-2}]
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PROG
| (PARI) a(n)=prod(k=0, n, prod(i=0, k, 2*i+1))
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CROSSREFS
| Cf. A000178, A005118.
Sequence in context: A099168 A004105 A060336 * A124488 A086683 A155203
Adjacent sequences: A057860 A057861 A057862 * A057864 A057865 A057866
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KEYWORD
| nonn
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AUTHOR
| Eric Weisstein (eric(AT)weisstein.com)
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EXTENSIONS
| Simpler description from Benoit Cloitre (benoit7848c(AT)orange.fr), May 03 2003
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