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a(n) = Product_{i=1..n, j=1..n} (i^4 - i^2*j^2 + j^4).
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%I #10 Nov 26 2023 12:44:29

%S 1,2704,4343072672016,104066856161782811235776987136,

%T 368057974579278182597141600363036562863943425064960000,

%U 1139317987311004502889916180807286481186277543437822119282797720728081762451885916160000

%N a(n) = Product_{i=1..n, j=1..n} (i^4 - i^2*j^2 + j^4).

%F a(n) ~ c * (2 + sqrt(3))^(sqrt(3)*n*(n+1)) * n^(4*n^2 - 1) / exp(6*n^2 - Pi*n*(n+1)/2), where c = 0.219927317102868518491484945565471919409874745762951216457178735860943437...

%t Table[Product[Product[i^4 - i^2*j^2 + j^4, {i, 1, n}], {j, 1, n}], {n, 1, 10}]

%o (Python)

%o from math import prod, factorial

%o def A367668(n): return (prod((k:=j**2)**2+(m:=i**2)*(m-k) 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. A203675, A324437, A367550.

%K nonn

%O 1,2

%A _Vaclav Kotesovec_, Nov 26 2023