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a(n) = (n^2 - n)!.
2

%I #19 Apr 17 2023 02:02:28

%S 1,1,2,720,479001600,2432902008176640000,

%T 265252859812191058636308480000000,

%U 1405006117752879898543142606244511569936384000000000,710998587804863451854045647463724949736497978881168458687447040000000000000

%N a(n) = (n^2 - n)!.

%C The next term has 104 digits.

%C For n > 0, a(n) is the number of n X n matrices using all the integers from 1 to n^2 and having the main diagonal given.

%H Winston de Greef, <a href="/A362187/b362187.txt">Table of n, a(n) for n = 0..21</a>

%F a(n) = (n^2 - n)*a(n-1) for n > 1.

%F a(n) = A000142(A002378(n-1)) for n > 0.

%t a[n_]:=(n^2-n)!; Array[a,9,0]

%Y Cf. A000142, A000290, A002378, A088020.

%Y Cf. A039622, A179268, A272094, A272095, A272164.

%Y Cf. A362209.

%K nonn,easy

%O 0,3

%A _Stefano Spezia_, Apr 10 2023