A272164 a(n) = Product_{k=0..n} (n^2-k)!.

1, 1, 288, 53094139822080000, 7114507432973653690572666462301501337370624000000000000

Offset: 0

Author

Vaclav Kotesovec, Apr 21 2016

Keywords

• nonn
• easy

Comments

The next term has 392 digits.

Crossrefs

Cf. A272095, A272163, A272238, A272241.

Programs

Mathematica

Table[Product[(n^2-k)!, {k, 0, n}], {n, 0, 6}]
Table[BarnesG[n^2 + 2]/BarnesG[n^2 - n + 1], {n, 0, 6}]

Formula

a(n) = A272163(n) * ((n^2)!)^(n+1) / A272179(n)^n.

a(n) ~ exp(1/24 + n/6 - n^2 - n^3) * n^(1 + n^2 + 2*n^3) * (2*Pi)^((n+1)/2).