A272168 a(n) = Product_{k=0..n} (k^2-k)!.

1, 1, 2, 1440, 689762304000, 1678124094566146045378560000000, 445127215203413988036981576746329306509322538188800000000000000

Offset: 0

Author

Vaclav Kotesovec, Apr 21 2016

Keywords

• nonn
• easy

Comments

The next term has 114 digits.

Crossrefs

Cf. A272094, A272167.

Programs

Mathematica

Table[Product[(k^2-k)!, {k, 0, n}], {n, 0, 8}]

Formula

a(n) ~ c * n^(n*(2*n^2 + 1)/3) * (2*Pi)^(n/2) / exp(5*n^3/9 + n/2 - Zeta(3) / (2*Pi^2)), where c = Product_{k>=2} (k*(k-1))!/stirling(k*(k-1)) = 1.086533635964823338078329042... and stirling(n) = sqrt(2*Pi*n) * n^n / exp(n) is the Stirling approximation of n!.