%I A065513
%S A065513 2,24,300,4320,72030,1376256,29760696,720000000,19292299290,
%T A065513 567575838720,18197320924068,631732166467584,23613833496093750,
%U A065513 945755921747804160,40410678374256222960,1835086247681868693504
%N A065513 Number of endofunctions of [n] with a cycle a->b->c->a and for all x 
               in [n], some iterate f^k(x)=a.
%F A065513 E.g.f.: T^3/3 where T=T(x) is Euler's tree function (see A000169).
%e A065513 a(4)=24: 1->2->3->1<-4; 2->3->1->2<-4; 3->1->2->3<-4 1->3->2->1<-4; 3->
               2->1->3<-4; 2->1->3->2<-4 (repeat with 1,2, then 3 excluded from 
               cycle)
%p A065513 T := x->-LambertW(-x); a := []; f := series((T(x))^3/3,x,24); for m from 
               1 to 24 do a := [op(a),op(2*m-1,f)*(m+2)! ] od; print(a);
%Y A065513 A000169 (unique cycle is length 1), A053506 (unique cycle has length 
               2)
%Y A065513 Sequence in context: A065101 A052739 A135389 this_sequence A119491 A001864 
               A099045
%Y A065513 Adjacent sequences: A065510 A065511 A065512 this_sequence A065514 A065515 
               A065516
%K A065513 nonn
%O A065513 3,1
%A A065513 Len Smiley (smiley(AT)math.uaa.alaska.edu), Nov 27 2001