A370200 a(n) = numerator((n!)^2/(2*(n-2)!*n^n)).

1, 2, 9, 48, 25, 2160, 2205, 17920, 5103, 18144000, 21175, 2874009600, 11293425, 100452352, 9577693125, 167382319104000, 253127875, 57621363351552000, 282135852999, 75676057600000, 372075093219375, 12364008005553684480000, 57618381445625, 11912609313278197235712

Offset

2,2

Comments

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

References

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

Links

Table of n, a(n) for n=2..25.

Mathematica

a[n_]:=Numerator[n!^2/(2(n-2)!n^n)]; Array[a, 24, 2]

Crossrefs

Cf. A000142, A000312, A001044, A370201 (denominators).

Sequence in context: A059272 A228341 A289576 * A369315 A223832 A323958

Adjacent sequences: A370197 A370198 A370199 * A370201 A370202 A370203

Keyword

nonn,frac

Author

Stefano Spezia, Feb 11 2024

Status

approved