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%I #11 Nov 22 2023 11:16:17
%S 3,1764,2905736652,66016970246853190656,
%T 64657853715047202043531429875379200,
%U 6627957368676918780503749855130249245999452089509478400
%N a(n) = Product_{i=1..n, j=1..n} (i^2 + i*j + j^2).
%F a(n) ~ c * 3^(3*n*(n+1)/2) * n^(2*n^2 - 2/3) / exp(3*n^2 - Pi*n*(n+1) / (2*sqrt(3))), where c = 3^(5/12) * exp(Pi/(12*sqrt(3))) * Gamma(1/3) / (2^(4/3) * Pi^(4/3)) = 0.42478290981890921418850643030484274341562970375995548434917...
%t Table[Product[Product[(i^2 + i*j + j^2), {i, 1, n}], {j, 1, n}], {n, 1, 10}]
%o (Python)
%o from math import prod, factorial
%o def A367542(n): return (prod(i*(i+j)+j**2 for i in range(1,n) for j in range(i+1,n+1))*factorial(n))**2*3**n # _Chai Wah Wu_, Nov 22 2023
%Y Cf. A203012, A324403, A367543.
%K nonn
%O 1,1
%A _Vaclav Kotesovec_, Nov 22 2023
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