|
|
A060908
|
|
E.g.f.: exp(x*exp(x*exp(x)) + 1/2*x^2*exp(x*exp(x))^2).
|
|
0
|
|
|
1, 1, 4, 25, 194, 1791, 19312, 237637, 3280524, 50136049, 839267936, 15255154179, 298936866736, 6277386102703, 140540145723720, 3339966073612921, 83936496568012208, 2223184658988286113, 61877234830148427808
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,3
|
|
COMMENTS
|
a(n) = the number of functions f:{1,2,...,n} -> {1,2,...,n} such that the functional digraphs have cycle lengths at most 2 and no element is at a distance of more than 2 form a cycle. - Geoffrey Critzer, Sep 23 2012
|
|
REFERENCES
|
I. P. Goulden and D. M. Jackson, Combinatorial Enumeration, Wiley, N.Y., 1983.
|
|
LINKS
|
|
|
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 = 2, m = 2.
|
|
MATHEMATICA
|
nn=20; a=x Exp[x]; b=x Exp[a]; t=Sum[n^(n-1)x^n/n! , {n, 1, nn}]; Range[0, nn]! CoefficientList[Series[Exp[b+b^2/2], {x, 0, nn}], x] (* Geoffrey Critzer, Sep 23 2012 *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|