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%I #17 Jun 24 2023 16:39:24
%S 1,3,240,1512000,1536288768000,429266120461516800000,
%T 50406068004584362019389440000000,
%U 3534677027377560888380072035048488960000000000,199761495428405897006583857561824669625759249203200000000000000
%N a(n) = Product_{i=1..n, j=1..n} (1 + i + j).
%F a(n) ~ A * 2^(2*n^2 + 4*n + 11/12) * n^(n^2 - 23/12) / (Pi * exp(3*n^2/2 + 1/12)), where A is the Glaisher-Kinkelin constant A074962.
%F a(n) = BarnesG(2*n + 3) / BarnesG(n + 3)^2.
%F Product_{i=1..n, j=1..n} (1 + 1/(i + j)) = a(n) / A079478(n) ~ 2^(2*n + 1) / (sqrt(Pi)*n^(3/2)). - _Vaclav Kotesovec_, Mar 29 2019
%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[1 + i + j, {i, 1, n}, {j, 1, n}], {n, 1, 10}]
%t Table[BarnesG[2*n + 3] / BarnesG[n + 3]^2, {n, 1, 10}]
%o (PARI) a(n) = prod(i=1, n, prod(j=1, n, 1+i+j)); \\ _Michel Marcus_, Feb 28 2019
%o (Magma) [(&*[(&*[1+k+j: j in [1..n]]): k in [1..n]]): n in [1..10]]; // _G. C. Greubel_, Feb 28 2019
%o (Sage) [product( product(1+k+j for j in (1..n)) for k in (1..n)) for n in (1..10)] # _G. C. Greubel_, Feb 28 2019
%Y Cf. A079478, A306594.
%K nonn
%O 0,2
%A _Vaclav Kotesovec_, Feb 28 2019
%E a(0)=1 prepended by _Alois P. Heinz_, Jun 24 2023
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