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a(n) = denominator((n!)^2/(2*(n-2)!*n^n)).
1

%I #7 Feb 14 2024 14:28:37

%S 2,3,16,125,108,16807,32768,531441,312500,2357947691,5971968,

%T 1792160394037,15818613944,320361328125,70368744177664,

%U 2862423051509815793,10167463313316,5480386857784802185939,64000000000000000,41209797661291758429,489272723587316370328

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

%C a(n) is the denominator of the probability that a sequence of n integers randomly chosen from [n] contains exactly n - 1 different integers (see Brualdi, pp. 57-58).

%D Richard A. Brualdi, Introductory Combinatorics, 5th ed. Pearson Education Inc., 2009.

%t a[n_]:=Denominator[n!^2/(2(n-2)!n^n)]; Array[a,21,2]

%Y Cf. A000142, A000312, A001044, A370200 (numerators).

%K nonn,frac

%O 2,1

%A _Stefano Spezia_, Feb 11 2024