A272166 -id:A272166 - cp's OEIS frontend

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

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

Offset: 0

Vaclav Kotesovec, Apr 20 2016

Cf. A272094, A272094, A272095.

Cf. A000178, A098694, A268196, A262261.

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

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.

A272165 a(n) = Product_{k=0..n} (k*n-k)^k.

Original entry on oeis.org

0, 4, 6912, 1632586752, 92771293593600000, 1922167968750000000000000000, 20386493620375898676722605059420979200000, 147691962494584259939724821292542617401603191419699200000

Offset: 1

Vaclav Kotesovec, Apr 21 2016

Cf. A272166.

Table[Product[(k*n-k)^k, {k, 1, n}], {n, 1, 10}]

a(n) ~ A * n^(n^2 + n + 1/12) / exp((n^2 + 2*n + 3)/4), where A = A074962 is the Glaisher-Kinkelin constant.

cp's OEIS Frontend

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

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