%I A053506
%S A053506 0,1,6,48,500,6480,100842,1835008,38263752,900000000,23579476910,
%T A053506 681091006464,21505924728444,737020860878848,27246730957031250,
%U A053506 1080863910568919040,45798768824157052688,2064472028642102280192
%N A053506 (n-1)*n^(n-2).
%C A053506 a(n) = number of endofunctions f of [n] which interchange a pair a<->
               b and for all x in [n] some iterate f^k(x) = a. E.g. a(3) = 6: 1<->
               2<-3; 3->1<->2; 2<->3<-1; 1->2<->3; 1<->3<-2; 2->1<->3. - Len Smiley 
               (smiley(AT)math.uaa.alaska.edu), Nov 27 2001
%C A053506 If offset is 0: right side of the binomial sum n-> sum( i^(i-1) * (n-i+1)^(n-i)*binomial(n, 
               i), i=1..n) - Yong Kong (ykong(AT)curagen.com), Dec 28 2000
%D A053506 A. P. Prudnikov, Yu. A. Brychkov and O.I. Marichev, "Integrals and Series", 
               Volume 1: "Elementary Functions", Chapter 4: "Finite Sums", New York, 
               Gordon and Breach Science Publishers, 1986-1992, Eq. (4.2.2.36)
%D A053506 R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see 
               Prop. 5.3.2.
%H A053506 Milan Janjic, <a href="http://www.pmfbl.org/janjic/">Enumerative Formulas 
               for Some Functions on Finite Sets</a>
%H A053506 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               GraphEdge.html">Graph Edge</a>
%F A053506 E.g.f.: 1/2!*LambertW(-x)^2. - Vladeta Jovovic (vladeta(AT)eunet.rs), 
               Apr 07 2001
%F A053506 E.g.f. if offset 0: W(-x)^2/((1+W(-x))*x), W(x) Lambert's function (principal 
               branch).
%F A053506 The sequence 1, 1, 6, 48 ... satisfies a(n)=(n(n+1)^n+0^n)/(n+1); it 
               is the main diagonal of A085388. - Paul Barry (pbarry(AT)wit.ie), 
               Jun 30 2003
%Y A053506 Cf. A000169, A000312, A053506-A053509.
%Y A053506 Sequence in context: A105627 A051578 A052639 this_sequence A055861 A052567 
               A002170
%Y A053506 Adjacent sequences: A053503 A053504 A053505 this_sequence A053507 A053508 
               A053509
%K A053506 nonn
%O A053506 1,3
%A A053506 N. J. A. Sloane (njas(AT)research.att.com), Jan 15 2000