A367550 a(n) = Product_{i=1..n, j=1..n} (i^4 + i^2*j^2 + j^4).

3, 63504, 2260442279270448, 3379470372507391964272022793486336, 2097229364987262298214192667129919538956418868293588090880000

Offset: 1

Author

Vaclav Kotesovec, Nov 22 2023

Keywords

• nonn

Crossrefs

Cf. A203673, A324437, A367542, A367543, A367668.

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 A367550(n): return (prod((i2:=i**2)*(i2+(j2:=j**2))+j2**2 for i in range(1,n) for j in range(i+1,n+1))*factorial(n)**2)**2*3**n # Chai Wah Wu, Nov 22 2023

Formula

a(n) = A367542(n) * A367543(n).

a(n) ~ Gamma(1/3)^3 * 3^(3*n*(n+1)/2 + 7/12) * n^(4*n^2 - 1) / (8*Pi^3 * exp(6*n^2 - (6*n*(n+1) + 1)*Pi/(4*sqrt(3)))).