OFFSET
0,3
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
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.
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 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Vladeta Jovovic, Apr 07 2001
STATUS
approved