%I #56 Nov 21 2024 07:49:03
%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
%C 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
%H Vincenzo Librandi, <a href="/A066274/b066274.txt">Table of n, a(n) for n = 1..300</a>
%H Milan Janjic, <a href="https://old.pmf.unibl.org/wp-content/uploads/2017/10/enumfun.pdf">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].
%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,changed
%O 1,2
%A _Len Smiley_, Dec 09 2001