A272238 a(n) = Product_{k=0..n} (n^2+k)!.

1, 2, 2073600, 25177856146146034974720000000, 14100949826093501607549529280892932893801777581548587107609477120000000000000000

Offset: 0

Author

Vaclav Kotesovec, Apr 23 2016

Keywords

• nonn
• easy

Comments

The next term has 173 digits.

Crossrefs

Cf. A135860, A272164, A272180, A272237, A272241.

Programs

Mathematica

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

Formula

a(n) = ((n^2+n)!)^(n+1) / A272237(n).

a(n) ~ exp(11/24 + n/6 - n^2 - n^3) * n^((1+n)*(1 + n + 2*n^2)) * (2*Pi)^((n+1)/2).