A371643 a(n) = Product_{k=0..n} (n^2 + k^2)!.

1, 2, 116121600, 52498561358549216844165257625600000000

Offset: 0

Author

Vaclav Kotesovec, Mar 31 2024

Keywords

• nonn

Comments

The next term has 107 digits.

Crossrefs

Cf. A296591, A371468, A371624.

Programs

Mathematica

Table[Product[(n^2+k^2)!, {k, 0, n}], {n, 0, 5}]

Formula

a(n) ~ 2^(4*n^3/3 + n^2 + 7*n/6 + 3/4) * exp(-26*n^3/9 + Pi*n^3/3 - 3*n^2/2 + Pi*n/4 - n) * Pi^((n+1)/2) * n^(8*n^3/3 + 3*n^2 + 4*n/3 + 1).