A065513 - OEIS

%I #21 Sep 08 2022 08:45:04

%S 2,24,300,4320,72030,1376256,29760696,720000000,19292299290,

%T 567575838720,18197320924068,631732166467584,23613833496093750,

%U 945755921747804160,40410678374256222960,1835086247681868693504,88263072551692077310386,4482662400000000000000000

%N Number of endofunctions of [n] with a cycle a->b->c->a and for all x in [n], some iterate f^k(x)=a.

%H Alois P. Heinz, <a href="/A065513/b065513.txt">Table of n, a(n) for n = 3..150</a>

%F E.g.f.: T^3/3 where T=T(x) is Euler's tree function (see A000169).

%F a(n) = (n-1)*(n-2)*n^(n-3). - _Vaclav Kotesovec_, Oct 05 2013

%F a(n) = 2*A053507(n). - _Vaclav Kotesovec_, Oct 07 2016

%e 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 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);

%t nn = 18; t = Sum[n^(n - 1) x^n/n!, {n, 1, nn}];

%t Range[0, nn]! CoefficientList[Series[2 t^3/3!, {x, 0, nn}], x] (* _Geoffrey Critzer_, Aug 14 2013 *)

%o (PARI) for(n=3,50, print1((n-1)*(n-2)*n^(n-3), ", ")) \\ _G. C. Greubel_, Nov 14 2017

%o (Magma) [(n-1)*(n-2)*n^(n-3): n in [3..50]]; // _G. C. Greubel_, Nov 14 2017

%Y Cf. A000169 (unique cycle is length 1), A053506 (unique cycle has length 2).

%Y Column k=3 of A201685.

%K nonn

%O 3,1

%A _Len Smiley_, Nov 27 2001