A060906 E.g.f.: exp(x*exp(x) + 1/3*x^3*exp(x)^3).

1, 1, 3, 12, 73, 556, 4737, 44122, 453441, 5186664, 65671201, 906052654, 13418086497, 211472682604, 3535616946513, 62621439810066, 1172370604136833, 23118679430573008, 478329265510033473, 10349724555927678934, 233633352312272612001, 5492655756487132979796

Offset: 0

Author

Vladeta Jovovic, Apr 07 2001

Keywords

• nonn

Comments

The number of functions from {1,2,...,n} to itself such that f(x)=f^4(x). - Geoffrey Critzer, Sep 18 2012

References

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

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..200

Crossrefs

Cf. A000949 - A000951, A060905 - A060913.

Column k=4 of A245501.

Programs

Mathematica

nn=20;a=x Exp[x];Range[0,nn]!CoefficientList[Series[Exp[a+a^3/3],{x,0,nn}],x] (* Geoffrey Critzer, Sep 18 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 = 1, m = 3.