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