A060913 E.g.f.: exp(x*exp(x*exp(x*exp(x))) + 1/3*x^3*exp(x*exp(x*exp(x)))^3).

1, 1, 3, 18, 157, 1656, 20727, 300784, 4955337, 91229616, 1853584651, 41147256624, 989990665677, 25647894553048, 711630284942319, 21049888453838136, 661180220075555473, 21976354057916680416

Offset: 0

Author

Vladeta Jovovic, Apr 07 2001

Keywords

• nonn

Comments

a(n) is the number of functions f:{1,2,...,n} -> {1,2,...,n} such that the functional digraphs have cycles of length 1 or 3 and no element is at a distance of more than 3 from a cycle. - Geoffrey Critzer, Sep 23 2012

References

• I. P. Goulden and D. M. Jackson, Combinatorial Enumeration, Wiley, N.Y., 1983.

Crossrefs

Cf. A000949-A000951, A060905-A060913.

Programs

Mathematica

nn=20; a=x Exp[x]; b=x Exp[a]; c=x Exp[b]; t=Sum[n^(n-1)x^n/n!, {n, 1, nn}]; Range[0,nn]! CoefficientList[Series[Exp[c+c^3/3], {x, 0, nn}], x] (* Geoffrey Critzer, Sep 23 2012 *)

Formula

E.g.f.: exp(Sum_{d|m} T_k^d/d), where T_k = x*exp(T_(k - 1)), k >= 1, T_0 = x; k = 3, m = 3.