A306728 a(n) = Product_{i=1..n, j=1..n} (i*(i+1) + j*(j+1)).

1, 4, 3072, 4682022912, 62745927042654535680, 22033340103629170301586112512000000, 479715049773154880180722813201712394999926095872000000, 1318058833735625830065875826842622254472987373414662267314001234660163584000000

Offset: 0

Author

Vaclav Kotesovec, Mar 06 2019

Keywords

• nonn

Crossrefs

Cf. A324403, A324443.

Programs

Mathematica

Table[Product[i*(i+1)+j*(j+1), {i, 1, n}, {j, 1, n}], {n, 0, 8}]

Python

from math import prod, factorial
def A306728(n): return (prod(i*(i+1)+j*(j+1) for i in range(1,n) for j in range(i+1,n+1))*factorial(n))**2*(n+1)<Chai Wah Wu, Nov 22 2023

Formula

a(n) ~ c * 2^(n*(n+2)) * exp(Pi*n*(n+2)/2 - 3*n^2) * n^(2*n^2 - 2 - Pi/4), where c = 0.4952828896469310726828820344381813905230827930914109676983577406850360879...