A371624 a(n) = Product_{k=0..n} (n^2 - k^2)!.

1, 1, 144, 1755758592000, 66052111513207347990207922176000000000

Offset: 0

Author

Vaclav Kotesovec, Mar 30 2024

Keywords

• nonn

Comments

The next term has 88 digits.

Crossrefs

Cf. A001142, A255322, A296591, A362288, A371603.

Programs

Mathematica

Table[Product[((2*n-k)*k)!, {k, 0, n}], {n, 0, 6}]
Table[Product[(n^2 - k^2)!, {k, 0, n}], {n, 0, 6}]

Formula

a(n) = (n^2)!^(n+1) / (A255322(n) * A371603(n)).

a(n) ~ c * A^(2*n) * 2^(4*n*(n^2 + 1)/3) * Pi^(n/2) * n^(4*n^3/3 + n^2 + 5*n/6 + 1/4) / exp(16*n^3/9 + n^2/2 + n), where c = 1.291409... = sqrt(2*Pi) / (A255504 * c from A371603) and A is the Glaisher-Kinkelin constant A074962.