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 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. 6
 2, 24, 300, 4320, 72030, 1376256, 29760696, 720000000, 19292299290, 567575838720, 18197320924068, 631732166467584, 23613833496093750, 945755921747804160, 40410678374256222960, 1835086247681868693504, 88263072551692077310386, 4482662400000000000000000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 3,1 LINKS Alois P. Heinz, Table of n, a(n) for n = 3..150 FORMULA E.g.f.: T^3/3 where T=T(x) is Euler's tree function (see A000169). a(n) = (n-1)*(n-2)*n^(n-3). - Vaclav Kotesovec, Oct 05 2013 a(n) = 2*A053507(n). - Vaclav Kotesovec, Oct 07 2016 EXAMPLE 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) MAPLE 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); MATHEMATICA nn = 18; t = Sum[n^(n - 1) x^n/n!, {n, 1, nn}]; Range[0, nn]! CoefficientList[Series[2 t^3/3!, {x, 0, nn}], x] (* Geoffrey Critzer, Aug 14 2013 *) PROG (PARI) for(n=3, 50, print1((n-1)*(n-2)*n^(n-3), ", ")) \\ G. C. Greubel, Nov 14 2017 (MAGMA) [(n-1)*(n-2)*n^(n-3): n in [3..50]]; // G. C. Greubel, Nov 14 2017 CROSSREFS Cf. A000169 (unique cycle is length 1), A053506 (unique cycle has length 2). Column k=3 of A201685. Sequence in context: A065101 A052739 A135389 * A246190 A246610 A119491 Adjacent sequences:  A065510 A065511 A065512 * A065514 A065515 A065516 KEYWORD nonn AUTHOR Len Smiley, Nov 27 2001 STATUS approved

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Last modified September 20 02:20 EDT 2019. Contains 327207 sequences. (Running on oeis4.)