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a(n) = Product_{i=1..n, j=1..n} (i*j + 1).
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%I #15 Jun 24 2023 15:58:15

%S 1,2,90,705600,4105057320000,52487876090562232320000,

%T 3487017405172854771910634342400000000,

%U 2448893405298238642974553493547144534294528000000000000,33257039167768610289435138215602132823918399655132218973388800000000000000000

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

%F 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.

%p a:= n-> mul(mul(i*j+1, i=1..n), j=1..n):

%p seq(a(n), n=0..9); # _Alois P. Heinz_, Jun 24 2023

%t Table[Product[i*j + 1, {i, 1, n}, {j, 1, n}], {n, 1, 10}]

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

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

%K nonn

%O 0,2

%A _Vaclav Kotesovec_, Mar 08 2019

%E a(0)=1 prepended by _Alois P. Heinz_, Jun 24 2023