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%I #3 Dec 10 2023 09:24:05
%S 1,5,12100,188898484500,91554454518735288960000,
%T 4263420404009649597344435073399120000000,
%U 46073465749493255153019723901007197815549903333795840000000000
%N a(n) = Product_{i=1..n, j=1..n} (i^2 + 3*i*j + j^2).
%F a(n) ~ 5^(5*n*(n+1)/2 + 1/2) * n^(2*n^2 - 1) / (2 * Pi * exp(3*n^2) * phi^(sqrt(5)*(n*(n+1) + 1/6) - 1/2)), where phi = A001622 is the golden ratio.
%t Table[Product[i^2 + 3*i*j + j^2, {i, 1, n}, {j, 1, n}], {n, 0, 7}]
%Y Cf. A367543, A324403, A367542, A079478^2, A368064, A368065, A368066.
%K nonn
%O 0,2
%A _Vaclav Kotesovec_, Dec 10 2023
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