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A066274 Number of endofunctions of [n] such that 1 is not a fixed point. 7
0, 2, 18, 192, 2500, 38880, 705894, 14680064, 344373768, 9000000000, 259374246010, 8173092077568, 279577021469772, 10318292052303872, 408700964355468750, 17293822569102704640, 778579070010669895696, 37160496515557841043456, 1874292305362402347591138 (list; graph; refs; listen; history; text; internal format)
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].

MAPLE

with(finance): seq(futurevalue(n-1, n-1, n-1), n=1..20); # Zerinvary Lajos, Mar 25 2009

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: A129627 A279860 A138413 * A052623 A155542 A157765

Adjacent sequences:  A066271 A066272 A066273 * A066275 A066276 A066277

KEYWORD

nonn

AUTHOR

Len Smiley, Dec 09 2001

STATUS

approved

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Last modified May 23 23:53 EDT 2017. Contains 286937 sequences.