A367543 a(n) = Product_{i=1..n, j=1..n} (i^2 - i*j + j^2).

1, 36, 777924, 51190934086656, 32435802373365731229926400, 483207398728525904876601066508152707481600, 350969035472356907726779584093506665415605824531908346799718400

Offset: 1

Author

Vaclav Kotesovec, Nov 22 2023

Keywords

• nonn

Crossrefs

Cf. A203312, A324403, A367542.

Cf. A324426, A079478.

Programs

Mathematica

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

Python

from math import prod, factorial
def A367543(n): return (prod(i*(i-j)+j**2 for i in range(1,n) for j in range(i+1,n+1))*factorial(n))**2 # Chai Wah Wu, Nov 22 2023

Formula

a(n) = A324426(n) / A079478(n).

a(n) ~ 3^(1/6) * Gamma(1/3)^2 * n^(2*n^2 - 1/3) / (2^(5/3) * Pi^(5/3) * exp(3*n^2 - (n^2 + n + 1/6)*Pi/sqrt(3))).