A324426 a(n) = Product_{i=1..n, j=1..n} (i^3 + j^3).

1, 2, 2592, 134425267200, 3120795915109442519040000, 180825857777547616919759624941086965760000000, 99356698720512072045648926659510730227553351200000695922065408000000000

Offset: 0

Author

Vaclav Kotesovec, Feb 27 2019

Keywords

• nonn

Crossrefs

Cf. A079478, A324403, A324437, A324438, A324439, A324440, A367834.

Cf. A272246, A307210, A367517, A367543.

Programs

Maple

a:= n-> mul(mul(i^3+j^3, i=1..n), j=1..n):
seq(a(n), n=0..7);  # Alois P. Heinz, Jun 24 2023

Mathematica

Table[Product[i^3+j^3, {i, 1, n}, {j, 1, n}], {n, 1, 10}]

PARI

a(n) = prod(i=1, n, prod(j=1, n, i^3+j^3)); \\ Michel Marcus, Feb 27 2019

Python

from math import prod, factorial
def A324426(n): return prod(i**3+j**3 for i in range(1,n) for j in range(i+1,n+1))**2*factorial(n)**3<Chai Wah Wu, Nov 26 2023

Formula

a(n) ~ A * 2^(2*n*(n+1) + 1/4) * exp(Pi*(n*(n+1) + 1/6)/sqrt(3) - 9*n^2/2 - 1/12) * n^(3*n^2 - 3/4) / (3^(5/6) * Pi^(1/6) * Gamma(2/3)^2), where A is the Glaisher-Kinkelin constant A074962.

a(n) = A079478(n) * A367543(n). - Vaclav Kotesovec, Nov 22 2023

For n>0, a(n)/a(n-1) = A272246(n)^2 / (2*n^9). - Vaclav Kotesovec, Dec 02 2023

Extensions

a(0)=1 prepended by Alois P. Heinz, Jun 24 2023