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A367543
a(n) = Product_{i=1..n, j=1..n} (i^2 - i*j + j^2).
14
1, 36, 777924, 51190934086656, 32435802373365731229926400, 483207398728525904876601066508152707481600, 350969035472356907726779584093506665415605824531908346799718400
OFFSET
1,2
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))).
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 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
CROSSREFS
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Nov 22 2023
STATUS
approved