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A296589 a(n) = Product_{k=0..n} binomial(2*n, k). 2
1, 2, 24, 1800, 878080, 2857680000, 63117561830400, 9577928124440387712, 10077943267571584204800000, 74054886893191804566576837427200, 3822038592032831128918160803430400000000, 1391938996758770867922655936144556115037409280000 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
Eric Weisstein's World of Mathematics, Barnes G-Function.
FORMULA
a(n) = ((2*n)!)^(n+1) / (n! * BarnesG(2*n + 2)).
a(n) ~ A * exp(n^2 + n - 1/24) / (2^(5/12) * Pi^((n+1)/2) * n^(n/2 + 5/12)), where A is the Glaisher-Kinkelin constant A074962.
MATHEMATICA
Table[Product[Binomial[2*n, k], {k, 0, n}], {n, 0, 12}]
Table[((2*n)!)^(n+1) / (n! * BarnesG[2*n + 2]), {n, 0, 12}]
CROSSREFS
Sequence in context: A292797 A163086 A280922 * A053995 A184595 A369678
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Dec 16 2017
EXTENSIONS
Missing a(0)=1 inserted by Georg Fischer, Nov 18 2021
STATUS
approved

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Last modified March 29 11:14 EDT 2024. Contains 371278 sequences. (Running on oeis4.)