A272093 a(n) = Product_{k=0..n} binomial(k*n,k).

1, 1, 12, 3780, 44844800, 26352845268750, 953083353075475894272, 2537540586421634737033298208000, 579150777545101402084349505293757972480000, 12933741941622730846344367593442776825612980847409218750, 31768605393074559234133528464091374346848946682424165820313600000000000

Offset: 0

Author

Vaclav Kotesovec, Apr 20 2016

Keywords

• nonn
• easy

Crossrefs

Cf. A272094, A272094, A272095.

Cf. A000178, A098694, A268196, A262261.

Programs

Mathematica

Table[Product[Binomial[k*n, k], {k, 0, n}], {n, 0, 10}]

Formula

a(n) = A272096(n) / (A272166(n) * A000178(n)).

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.