A081131 a(n) = n^(n-2) * binomial(n,2).

0, 0, 1, 9, 96, 1250, 19440, 352947, 7340032, 172186884, 4500000000, 129687123005, 4086546038784, 139788510734886, 5159146026151936, 204350482177734375, 8646911284551352320, 389289535005334947848, 18580248257778920521728, 937146152681201173795569

Offset: 0

Author

Paul Barry, Mar 08 2003

Keywords

• easy
• nonn

Comments

Main diagonal of A081130.

a(n) is the number of partial functions f: {1,2,...,n} -> {1,2,...,n} that have exactly 2 undefined elements. - Geoffrey Critzer, Feb 08 2012

a(n+1) is the determinant of the circulant matrix having (n-1, n-2, ..., 0) as first row, for n >= 1. See A070896 for a variant, and A303260 for a related sequence. - M. F. Hasler, Apr 23 2018

a(n) is the number of birooted labeled trees on n nodes. - Brendan McKay, May 01 2018

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200

Crossrefs

Cf. A070896, A081129, A081130, A303260.

Sequences of the form (n+m)^n*binomial(n+2,2): A081133 (m=0), A081132 (m=1), this sequence (m=2), A053507 (m=3), A081196 (m=4).

Programs

Magma

[n lt 2 select 0 else n^(n-2)*Binomial(n,2): n in [0..20]]; // G. C. Greubel, May 18 2021

Mathematica

Join[{0},Table[n^(n-2) Binomial[n, 2], {n, 1, 20}]] (* Vladimir Joseph Stephan Orlovsky, Apr 19 2011 *)

Sage

[0 if (n<2) else n^(n-2)*binomial(n,2) for n in (0..20)] # G. C. Greubel, May 18 2021

Formula

a(0) = a(1) = 0, a(n) = n^(n-2)*binomial(n,2).

E.g.f.: T(x)^2/(2*(1-T(x))) where T(x) is the e.g.f. for A000169. - Geoffrey Critzer, Feb 08 2012