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%I #8 Nov 26 2023 12:59:07
%S 1,1936,1765124816400,19271059559619728900751360000,
%T 25048411180596698786915756280274804766474649600000000,
%U 23045227505577134384745253646275782332295626096040088365089618773238077194240000000000
%N a(n) = Product_{i=1..n, j=1..n} (i^4 - i^3*j + i^2*j^2 - i*j^3 + j^4).
%F a(n) = A324438(n) / A079478(n).
%F a(n) ~ c * n^(4*n^2 - 5/6) * phi^(sqrt(5)*n*(n+1)) / exp(6*n^2 - sqrt(phi)*Pi*n*(n+1)/5^(1/4)), where phi = A001622 is the golden ratio and c = 0.2505211390193028244009922677012518708897316924498037078191143761182342931773594...
%t Table[Product[i^4 - i^3*j + i^2*j^2 - i*j^3 + j^4, {i, 1, n}, {j, 1, n}], {n, 1, 6}]
%o (Python)
%o from math import prod, factorial
%o def A367679(n): return (prod(i*(i*(i*(i-j)+j**2)-j**3)+j**4 for i in range(1,n) for j in range(i+1,n+1))*factorial(n)**2)**2 # _Chai Wah Wu_, Nov 26 2023
%Y Cf. A079478, A324437, A324438, A367550, A367668.
%K nonn
%O 1,2
%A _Vaclav Kotesovec_, Nov 26 2023
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