A371468 a(n) = Product_{k=0..n} (n^3 + k^3)!.

1, 2, 306128067620555980800000

Offset: 0

Author

Vaclav Kotesovec, Apr 01 2024

Keywords

• nonn

Comments

The next term a(3) has 169 digits.

Crossrefs

Cf. A296591, A371643, A371646.

Programs

Mathematica

Table[Product[(n^3 + k^3)!, {k, 0, n}], {n, 0, 5}]

Formula

a(n) ~ 2^(2*n^4 + n^3 + n^2/4 + 3*n/2 + 89/120) * Pi^((n+1)/2) * exp(Pi*sqrt(3)*n^4/4 - 59*n^4/16 - 3*n^3/2 - 3*n/2 + Pi*n/(2*sqrt(3)) - 9/320) * n^(15*n^4/4 + 9*n^3/2 + 3*n^2/4 + 3*n/2 + 3/2).