A324439 a(n) = Product_{i=1..n, j=1..n} (i^6 + j^6).

1, 2, 1081600, 528465082730906880000, 29276520893554373473343522853366005760000000000, 5719545329208791496596894540018824083491259163047733746620041978183680000000000000000

Offset: 0

Author

Vaclav Kotesovec, Feb 28 2019

Keywords

• nonn

Crossrefs

Cf. A079478, A324403, A324426, A324437, A324438, A324440, A367834.

Cf. A367668, A367823.

Programs

Maple

a:= n-> mul(mul(i^6 + j^6, i=1..n), j=1..n):
seq(a(n), n=0..5);  # Alois P. Heinz, Nov 26 2023

Mathematica

Table[Product[i^6 + j^6, {i, 1, n}, {j, 1, n}], {n, 1, 6}]

Python

from math import prod, factorial
def A324439(n): return (prod(i**6+j**6 for i in range(1,n) for j in range(i+1,n+1))*factorial(n)**3)**2<Chai Wah Wu, Nov 26 2023

Formula

a(n) ~ c * 2^(n*(n+1)) * (2 + sqrt(3))^(sqrt(3)*n*(n+1)) * exp(Pi*n*(n+1) - 9*n^2) * n^(6*n^2 - 3/2), where c = 0.104143806044091748191387307161835081649...

a(n) = A324403(n) * A367668(n). - Vaclav Kotesovec, Dec 01 2023

For n>0, a(n)/a(n-1) = A367823^2 / (2*n^18). - Vaclav Kotesovec, Dec 02 2023

Extensions

a(n)=1 prepended by Alois P. Heinz, Nov 26 2023