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%I #23 Feb 21 2024 14:42:23
%S 1,12,120960,5230697472000,3102242008666197196800000,
%T 61998887798316869577999908025139200000000,
%U 86897409147752508696036023331613625269650404482744320000000000,15860866523235520512929173666895185100358189521818149024850236796901838028800000000000000
%N a(n) = n*(n^2 - 1)!.
%C a(n) is the number of ways to fill an n X n square matrix with n^2 distinct elements such that a chosen element is in a designated row (or alternatively a column).
%F a(n) = (n^2)!/n.
%F a(n) = Integral_{x>=0} x^(n - 1)*exp(-x^(1/n)) dx.
%p seq(n*factorial(n^2-1), n=1..8);
%t Table[n*(n^2-1)!, {n, 1, 8}]
%o (PARI) a(n) = n*(n^2-1)!
%Y Cf. A088020, A179268.
%K nonn,easy
%O 1,2
%A _Thomas Scheuerle_, Jan 25 2024