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%I #4 Dec 10 2023 09:25:33
%S 1,6,24336,870746557824,1311726482483997806493696,
%T 256433546267136937832915286844640487014400,
%U 15678550451426175377500759401206644047210595564950427820202393600
%N a(n) = Product_{i=1..n, j=1..n} (i^2 + 4*i*j + j^2).
%F a(n) ~ 2^((3+sqrt(3))*n*(n+1) + (sqrt(3)-1)/6) * 3^(3*n*(n+1) + 13/24) * n^(2*n^2 - 7/6) / (Gamma(1/3)^(1/2) * Gamma(1/4)^(1/3) * Pi^(7/12) * (1 + sqrt(3))^((6*n*(n+1) + 1)/sqrt(3) - 1/2) * exp(3*n^2)).
%t Table[Product[i^2 + 4*i*j + j^2, {i, 1, n}, {j, 1, n}], {n, 0, 7}]
%Y Cf. A367543, A324403, A367542, A079478^2, A368067, A368065, A368066.
%K nonn
%O 0,2
%A _Vaclav Kotesovec_, Dec 10 2023