OFFSET
1,1
FORMULA
a(n) ~ c * 3^(3*n*(n+1)/2) * n^(2*n^2 - 2/3) / exp(3*n^2 - Pi*n*(n+1) / (2*sqrt(3))), where c = 3^(5/12) * exp(Pi/(12*sqrt(3))) * Gamma(1/3) / (2^(4/3) * Pi^(4/3)) = 0.42478290981890921418850643030484274341562970375995548434917...
MATHEMATICA
Table[Product[Product[(i^2 + i*j + j^2), {i, 1, n}], {j, 1, n}], {n, 1, 10}]
PROG
(Python)
from math import prod, factorial
def A367542(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*3**n # Chai Wah Wu, Nov 22 2023
CROSSREFS
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Nov 22 2023
STATUS
approved