A272244 a(n) = Product_{k=0..n} (n^2 + k^2).

0, 2, 160, 21060, 4352000, 1313845000, 547573478400, 301758856490000, 212663770808320000, 186659516597629140000, 199722414913149440000000, 255947740845844788169000000, 387074162712817024892928000000, 682170272459193898736228210000000

Offset: 0

Author

Vaclav Kotesovec, Apr 23 2016

Keywords

• nonn
• easy

Crossrefs

Cf. A126804, A272246, A272247, A272248, A367823, A367833.

Cf. A101686, A272180, A323540, A324403.

Programs

Mathematica

Table[Product[n^2+k^2,{k,0,n}],{n,0,15}]

Formula

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