A367670 a(n) = Product_{i=1..n, j=1..n} (i^8 + i^4*j^4 + j^8).

3, 171714816, 9817265089769041882465383168, 351690857158733335833718073682368165890982417955022627663773696

Offset: 1

Author

Vaclav Kotesovec, Nov 26 2023

Keywords

• nonn

Crossrefs

Cf. A367542, A367543, A367550, A367668.

Programs

Mathematica

Table[Product[Product[i^8 + i^4*j^4 + j^8, {i, 1, n}], {j, 1, n}], {n, 1, 7}]

Python

from math import prod, factorial
def A367670(n): return (prod((k:=j**4)**2+(m:=i**4)*(m+k) for i in range(1,n) for j in range(i+1,n+1))*factorial(n)**4)**2*3**n # Chai Wah Wu, Nov 26 2023

Formula

a(n) = A367550(n) * A367668(n).

a(n) = A367542(n) * A367543(n) * A367668(n).

a(n) ~ c * 3^(3*n*(n+1)/2) * (2 + sqrt(3))^(sqrt(3)*n*(n+1)) * n^(8*n^2 - 2) / exp(12*n^2 - Pi*(1 + sqrt(3))*n*(n+1)/2), where c = 0.05091893538977858024246640150391280389386566805866250210433631511020673755...