|
%I #11 Apr 23 2016 08:04:32
%S 1,1,24,27216,1956864000,11593630125000000,7004354761049263478784000,
%T 515246658615545697034849051407876096,
%U 5368556637668593177532650186945239827409750982656,9038577429104951379916309583338181472480254559457860096000000000
%N a(n) = Product_{k=0..n} binomial(n^2,k).
%F a(n) = ((n^2)!)^(n+1) / (A272164(n) * A000178(n)).
%F a(n) ~ A * exp(3*n^2/4 + 5*n/6 - 1/8) * n^(n^2/2 - 5/12) / (2*Pi)^((n+1)/2), where A = A074962 is the Glaisher-Kinkelin constant.
%t Table[Product[Binomial[n^2, k], {k, 0, n}], {n, 0, 10}]
%t Table[((n^2)!)^(n+1) * BarnesG[n^2 - n + 1] / (BarnesG[n^2 + 2] * BarnesG[n+2]), {n, 0, 10}]
%Y Cf. A272093, A272094, A272241.
%Y Cf. A000178, A098694, A268196, A262261.
%K nonn,easy
%O 0,3
%A _Vaclav Kotesovec_, Apr 20 2016
|
