A306760 a(n) = Product_{i=1..n, j=1..n} (i*j + 1).

1, 2, 90, 705600, 4105057320000, 52487876090562232320000, 3487017405172854771910634342400000000, 2448893405298238642974553493547144534294528000000000000, 33257039167768610289435138215602132823918399655132218973388800000000000000000

Offset: 0

Author

Vaclav Kotesovec, Mar 08 2019

Keywords

• nonn

Crossrefs

Cf. A079478, A101686, A185141, A324444, A306765, A324589, A306907.

Programs

Maple

a:= n-> mul(mul(i*j+1, i=1..n), j=1..n):
seq(a(n), n=0..9);  # Alois P. Heinz, Jun 24 2023

Mathematica

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

Formula

a(n) ~ c * n^(n*(2*n+1) + 2*gamma) * (2*Pi)^n * exp(1/6 + log(n)^2 - 2*n^2), where c = 1/A306765 and gamma is the Euler-Mascheroni constant A001620.

Extensions

a(0)=1 prepended by Alois P. Heinz, Jun 24 2023