A367517 a(n) = Product_{1 <= i < j <= n} (i^3 + j^3).

1, 9, 8820, 3756261600, 1808353823416358400, 2039434890206782239939575808000, 9701283544768145414379038964290421034844160000, 318565016660642285381616434022976430918222575100233223503872000000

Offset: 1

Author

Vaclav Kotesovec, Nov 21 2023

Keywords

• nonn

Crossrefs

Cf. A203475, A324426.

Cf. A093883, A203312.

Programs

Mathematica

Table[Product[Product[i^3 + j^3, {i,1,j-1}], {j,2,n}], {n,1,10}]

Python

from math import prod
def A367517(n): return prod(i**3+j**3 for i in range(1,n) for j in range(i+1,n+1)) # Chai Wah Wu, Nov 22 2023

Formula

a(n) ~ c * 2^(n^2 + n/2) * n^(3*n*(n-1)/2 - 9/8) / exp(9*n^2/4 - Pi*n*(n+1) / (2*sqrt(3)) - 3*n/2), where c = 0.1474592465511237361695489773766942970580292170583524962797073759996256...

a(n) = A093883(n) * A203312(n).