OFFSET
0,2
LINKS
Eric Weisstein's World of Mathematics, Barnes G-Function.
Wikipedia, 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
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Dec 16 2017
EXTENSIONS
Missing a(0)=1 inserted by Georg Fischer, Nov 18 2021
STATUS
approved