A065888 a(n) = number of endofunctions on [n] with a 4-cycle a->b->c->d->a and for any x in [n], some iterate f^k(x) = a.

6, 120, 2160, 41160, 860160, 19840464, 504000000, 14030763120, 425681879040, 13997939172360, 496360987938816, 18891066796875000, 768426686420090880, 33279382190563948320, 1529238539734890577920, 74326797938267012471904

Offset: 4

Author

Len Smiley, Nov 27 2001

Keywords

• nonn

Examples

			a(4) = 6 : 3 [choices of 1's opposite in cycle] * 2 [choices of 1's image]
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 4..150

Crossrefs

Cf. A000169 (1-cycle), A053506 (2-cycle), A065513 (3-cycle), A065889 (= A065888/2: underlying simple graphs).

Programs

Mathematica

Rest[Rest[Rest[Rest[CoefficientList[Series[(LambertW[-x])^4/4, {x, 0, 20}], x]* Range[0, 20]!]]]] (* Vaclav Kotesovec, Oct 05 2013 *)
Table[(n-1)(n-2)(n-3)n^(n-4),{n,4,20}] (* Harvey P. Dale, Dec 04 2015 *)

Formula

E.g.f.: T^4/4 where T = T(x) is Euler's tree function (see A000169).

a(n) = (n-1)*(n-2)*(n-3)*n^(n-4). - Vaclav Kotesovec, Oct 05 2013