%I #6 Nov 22 2023 11:15:59
%S 1,36,777924,51190934086656,32435802373365731229926400,
%T 483207398728525904876601066508152707481600,
%U 350969035472356907726779584093506665415605824531908346799718400
%N a(n) = Product_{i=1..n, j=1..n} (i^2 - i*j + j^2).
%F a(n) = A324426(n) / A079478(n).
%F a(n) ~ 3^(1/6) * Gamma(1/3)^2 * n^(2*n^2 - 1/3) / (2^(5/3) * Pi^(5/3) * exp(3*n^2 - (n^2 + n + 1/6)*Pi/sqrt(3))).
%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 A367543(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 # _Chai Wah Wu_, Nov 22 2023
%Y Cf. A203312, A324403, A367542.
%Y Cf. A324426, A079478.
%K nonn
%O 1,2
%A _Vaclav Kotesovec_, Nov 22 2023