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)*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
MATHEMATICA
Join[{0}, Table[n^(n-2) Binomial[n, 2], {n, 1, 20}]] (* Vladimir Joseph Stephan Orlovsky, Apr 19 2011 *)
PROG
(Magma) [n lt 2 select 0 else n^(n-2)*Binomial(n, 2): n in [0..20]]; // G. C. Greubel, May 18 2021
(Sage) [0 if (n<2) else n^(n-2)*binomial(n, 2) for n in (0..20)] # G. C. Greubel, May 18 2021
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Mar 08 2003
STATUS
approved