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A066274 Number of endofunctions of [n] such that 1 is not a fixed point. 7

%I

%S 0,2,18,192,2500,38880,705894,14680064,344373768,9000000000,

%T 259374246010,8173092077568,279577021469772,10318292052303872,

%U 408700964355468750,17293822569102704640,778579070010669895696,37160496515557841043456,1874292305362402347591138

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

%C a(n) is the number of functional digraphs that are not a solitary rooted tree. - _Geoffrey Critzer_, Aug 31 2013

%C For n > 1 a(n) is the number of numbers with n digits in base n. - _Gionata Neri_, Feb 18 2016

%H Vincenzo Librandi, <a href="/A066274/b066274.txt">Table of n, a(n) for n = 1..300</a>

%H Milan Janjic, <a href="http://www.pmfbl.org/janjic/">Enumerative Formulas for Some Functions on Finite Sets</a>

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

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

%F For n > 1 a(n)=1/(Integral_{x=n..infinity} 1/x^n dx). - _Francesco Daddi_, Aug 01 2011

%F a(n) = sum(i=1..n-1, C(n,i)*(i^i*(n-i)^(n-i-1))). - _Vladimir Kruchinin_ May 15 2013

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

%F a(n) = 2*A081131(n) = 2*|A070896(n)|. - _Geoffrey Critzer_, Aug 31 2013

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

%p with(finance): seq(futurevalue(n-1, n-1, n-1), n=1..20); # _Zerinvary Lajos_, Mar 25 2009

%t Table[(n-1)*n^(n-1), {n, 1, 20}] (* _Vladimir Joseph Stephan Orlovsky_, Apr 19 2011 *)

%o (MAGMA) [n^n - n^(n-1): n in [1..20]]; // _Vincenzo Librandi_, Aug 02 2011

%Y Cf. A045531, A066275.

%K nonn

%O 1,2

%A _Len Smiley_, Dec 09 2001

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Last modified October 16 13:12 EDT 2018. Contains 316263 sequences. (Running on oeis4.)