A060907 E.g.f.: exp(x*exp(x) + 1/2*x^2*exp(x)^2 + 1/4*x^4*exp(x)^4).

1, 1, 4, 19, 116, 901, 8422, 89755, 1061048, 13746169, 193901066, 2965146559, 48946004956, 867463969789, 16405240966766, 329147315037811, 6973157545554128, 155446026607476145, 3636697161715448914, 89099916704329731895, 2281451214192505136516

Offset: 0

Author

Vladeta Jovovic, Apr 07 2001

Keywords

• nonn

Comments

The number of functions from {1,2,...,n} into itself such that f(x) = f^5(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=5 of A245501.

Programs

Maple

egf:= exp(x*exp(x)+x^2*exp(x)^2/2+x^4*exp(x)^4/4):
a:= n-> n!*coeff(series(egf, x, n+11), x, n):
seq(a(n), n=0..25);  # Alois P. Heinz, Jul 25 2014

Mathematica

nn=20;a=x Exp[x];Range[0,nn]!CoefficientList[Series[Exp[a+a^2/2+a^4/4],{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 = 4.