A370483 a(n) = Product_{k=0..n} binomial(n^2 + k^2, k^2).

1, 2, 350, 347633000, 101143578356902991250, 422044560230008480282938965899488406272, 1208807563912714402070105775158111317516306396248661153276031151000

Offset: 0

Author

Vaclav Kotesovec, Mar 31 2024

Keywords

• nonn

Crossrefs

Cf. A255322, A371643.

Programs

Mathematica

Table[Product[Binomial[n^2 + k^2, n^2], {k, 0, n}], {n, 0, 8}]
Table[Product[Binomial[n^2 + k^2, k^2], {k, 0, n}], {n, 0, 8}]

Formula

a(n) = Product_{k=0..n} binomial(n^2 + k^2, n^2).

a(n) = A371643(n) / ((n^2)!^(n+1) * A255322(n)).

a(n) ~ 2^(4*n^3/3 + n^2 + n/6 + 1/4) * exp((Pi-4)*n^3/3 + Pi*n/4) / (A255504 * n^(n + 1/2) * Pi^(n/2)).