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

Author

Len Smiley, Dec 09 2001

Keywords

• nonn

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

a(n) is the number of pairs of adjacent equal letters in all n-ary words of length n. - John Tyler Rascoe, Nov 19 2024

Examples

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

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..300
• Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets

Crossrefs

Cf. A045531, A066275.

Programs

Magma

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

Mathematica

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

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