A367542 a(n) = Product_{i=1..n, j=1..n} (i^2 + i*j + j^2).

3, 1764, 2905736652, 66016970246853190656, 64657853715047202043531429875379200, 6627957368676918780503749855130249245999452089509478400

Offset

1,1

Links

Table of n, a(n) for n=1..6.

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

Cf. A203012, A324403, A367543.

Sequence in context: A262500 A290944 A116994 * A172940 A096730 A255862

Adjacent sequences: A367539 A367540 A367541 * A367543 A367544 A367545

Keyword

nonn

Author

Vaclav Kotesovec, Nov 22 2023

Status

approved