A066274 Number of endofunctions of [n] such that 1 is not a fixed point.

0, 2, 18, 192, 2500, 38880, 705894, 14680064, 344373768, 9000000000, 259374246010, 8173092077568, 279577021469772, 10318292052303872, 408700964355468750, 17293822569102704640, 778579070010669895696, 37160496515557841043456, 1874292305362402347591138

Offset

1,2

Comments

a(n) is the number of functional digraphs that are not a solitary rooted tree. - Geoffrey Critzer, Aug 31 2013

For n > 1 a(n) is the number of numbers with n digits in base n. - Gionata Neri, Feb 18 2016

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..300

Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets

Formula

a(n) = n^n - n^(n-1).

E.g.f.: T^2/(1-T), where T=T(x) is Euler's tree function (see A000169).

For n > 1 a(n)=1/(Integral_{x=n..infinity} 1/x^n dx). - Francesco Daddi, Aug 01 2011

a(n) = sum(i=1..n-1, C(n,i)*(i^i*(n-i)^(n-i-1))). - Vladimir Kruchinin May 15 2013

E.g.f.: x^2*A''(x) where A(x) is the e.g.f. for A000272. - Geoffrey Critzer, Aug 31 2013

a(n) = 2*A081131(n) = 2*|A070896(n)|. - Geoffrey Critzer, Aug 31 2013

Example

a(2)=2: [1->2,2->1], [1->2,2->2].

Mathematica

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

Prog

(Magma) [n^n - n^(n-1): n in [1..20]]; // Vincenzo Librandi, Aug 02 2011

Crossrefs

Cf. A045531, A066275.

Sequence in context: A279860 A362731 A138413 * A052623 A362992 A155542

Adjacent sequences: A066271 A066272 A066273 * A066275 A066276 A066277

Keyword

nonn

Author

Len Smiley, Dec 09 2001

Status

approved