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%I #14 Dec 28 2023 03:01:14
%S 1,2,180,6652800,402265543680000,109211487076824381849600000,
%T 295382703175843424854047228769075200000000,
%U 15385012566245626089929288743828190926813939944652800000000000
%N a(n) = Product_{i=1..n, j=1..n} (i^2 + j).
%F From _Vaclav Kotesovec_, Dec 27 2023: (Start)
%F a(n) ~ c * n^(2*n^2 + n/2 - 1/4) / exp(2*n^2 - 2*Pi*n^(3/2)/3 - Pi*sqrt(n)/2), where c = 0.31906...
%F For n>1, a(n) = a(n-1) * Gamma(n - i*sqrt(n)) * Gamma(n + i*sqrt(n)) * Gamma(n^2 + n + 1) * sinh(Pi*sqrt(n)) / (Pi * n^(5/2) * Gamma(n^2)), where i is the imaginary unit. (End)
%p a:= n-> mul(mul(i^2+j, i=1..n), j=1..n):
%p seq(a(n), n=0..8); # _Alois P. Heinz_, Jun 24 2023
%t Table[Product[i^2 + j, {i, 1, n}, {j, 1, n}], {n, 1, 10}]
%t Table[Product[Pochhammer[1 + i^2, n], {i, 1, n}], {n, 1, 10}]
%Y Cf. A079478, A101686, A255322, A324403.
%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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