A367942 a(n) = Product_{i=1..n, j=1..n} (i^2 + 3*j^2).

1, 4, 5824, 45861064704, 9751658280030585225216, 176005320076923781520069562958715289600, 656508955366282248103393001602851493819854909361664242483200

Offset: 0

Author

Vaclav Kotesovec, Dec 05 2023

Keywords

• nonn

Crossrefs

Cf. A324403, A367941, A367943, A367944.

Cf. A367542, A367543.

Programs

Mathematica

Table[Product[i^2+3*j^2, {i, 1, n}, {j, 1, n}], {n, 0, 8}]

Formula

a(n) ~ c * n^(2*n^2 - 1/2) * 4^(n*(n+1)) * 3^(-n/2) * exp(5*Pi*n*(n+1)/(6*sqrt(3)) - 3*n^2), where c = 0.4612030005343304845802441101292774353695846313857765074861837886133930626...