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

%I #6 Dec 07 2023 02:18:52

%S 1,4,5824,45861064704,9751658280030585225216,

%T 176005320076923781520069562958715289600,

%U 656508955366282248103393001602851493819854909361664242483200

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

%F 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...

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

%Y Cf. A324403, A367941, A367943, A367944.

%Y Cf. A367542, A367543.

%K nonn

%O 0,2

%A _Vaclav Kotesovec_, Dec 05 2023