|
%I #8 Apr 21 2016 16:51:18
%S 1,1,12,3780,44844800,26352845268750,953083353075475894272,
%T 2537540586421634737033298208000,
%U 579150777545101402084349505293757972480000,12933741941622730846344367593442776825612980847409218750,31768605393074559234133528464091374346848946682424165820313600000000000
%N a(n) = Product_{k=0..n} binomial(k*n,k).
%F a(n) = A272096(n) / (A272166(n) * A000178(n)).
%F a(n) ~ A^2 * exp(n^2/2 + 3*n/4 + 1/12) * n^(n^2/2 - 1/3) / (2*Pi)^((n+1)/2), where A = A074962 is the Glaisher-Kinkelin constant.
%t Table[Product[Binomial[k*n, k], {k, 0, n}], {n, 0, 10}]
%Y Cf. A272094, A272094, A272095.
%Y Cf. A000178, A098694, A268196, A262261.
%K nonn,easy
%O 0,3
%A _Vaclav Kotesovec_, Apr 20 2016
|
