A367668 a(n) = Product_{i=1..n, j=1..n} (i^4 - i^2*j^2 + j^4).

1, 2704, 4343072672016, 104066856161782811235776987136, 368057974579278182597141600363036562863943425064960000, 1139317987311004502889916180807286481186277543437822119282797720728081762451885916160000

Offset: 1

Author

Vaclav Kotesovec, Nov 26 2023

Keywords

• nonn

Crossrefs

Cf. A203675, A324437, A367550.

Programs

Mathematica

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

Python

from math import prod, factorial
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

Formula

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...