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%I #24 Aug 08 2023 04:33:21
%S 1,16,108864,2391175987200,615524208068689920000000,
%T 4831082166102613213870122703257600000000,
%U 2481336275198061145749280386508780674949224836628480000000000
%N a(n) = (n^2)!*(n!)^2/(2*n-1)!.
%C a(n) is the number of square matrices of size n, whose elements are a permutation of 1, 2, ..., n^2, having a saddle point.
%H A. J. Goldman, <a href="https://www.jstor.org/stable/2309755">The probability of a saddlepoint</a>, The American Mathematical Monthly, 64, 10 (1957), pp. 729-730.
%H E. D. Thorp, <a href="http://www.edwardothorp.com/wp-content/uploads/2016/11/TheProbabilityThatAMatrixHasASaddlePoint.pdf">The probability that a matrix has a saddle point</a>, Information Sciences 19 2 (1979), 91-95.
%K nonn
%O 1,2
%A _Sela Fried_, Aug 07 2023