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A081131 a(n) = n^(n-2) * C(n,2). 10
0, 0, 1, 9, 96, 1250, 19440, 352947, 7340032, 172186884, 4500000000, 129687123005, 4086546038784, 139788510734886, 5159146026151936, 204350482177734375, 8646911284551352320, 389289535005334947848, 18580248257778920521728 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

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

FORMULA

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

MATHEMATICA

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

CROSSREFS

Cf. A070896, A081129, A081130, A303260.

Sequence in context: A024116 A264208 A070896 * A158489 A069636 A069621

Adjacent sequences:  A081128 A081129 A081130 * A081132 A081133 A081134

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Mar 08 2003

STATUS

approved

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Last modified August 18 12:35 EDT 2018. Contains 313832 sequences. (Running on oeis4.)