A371642 a(n) = Product_{k=0..n} (n^2 + k^2)! / (n^2 - k^2)!.

1, 2, 806400, 29900785676206001356800000, 1118776785681133797769642926006209350326602179759885516800000000000000

Offset: 0

Author

Vaclav Kotesovec, Mar 31 2024

Keywords

• nonn

Crossrefs

Cf. A272241, A371624, A371643.

Programs

Mathematica

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

Formula

a(n) = A371643(n) / A371624(n).

a(n) ~ c * 2^(n^2 - n/6 + 1/4) * exp((3*Pi-10)*n^3/9 - n^2 + Pi*n/4) * n^(4*n^3/3 + 2*n^2 + n/2 + 3/4) / A^(2*n), where c = 1.941002... = A255504 * (c from A371603) and A is the Glaisher-Kinkelin constant A074962.