OFFSET
0,3
COMMENTS
Here, a component of f is a weakly connected component of its functional digraph.
FORMULA
G.f.: 1/ (1 - A(x)) where A(x) is the o.g.f. for A001865.
EXAMPLE
a(3)=24 because there are 27 functions f:{1,2,3}->{1,2,3} but three of these are not counted: 1->3 2->2 3->3; 1->3 2->2 3->1; 1->1 2->2 3->1.
MATHEMATICA
nn=20; t= Sum[n^(n-1)x^n/n!, {n, 1, nn}]; a=Range[0, nn]! CoefficientList[Series[Log[1/(1-t)], {x, 0, nn}], x]; b=Sum[a[[i]]x^(i-1), {i, 1, nn+1}]; CoefficientList[Series[1/(1-b), {x, 0, nn}], x]
CROSSREFS
KEYWORD
nonn
AUTHOR
Geoffrey Critzer, Nov 21 2012
STATUS
approved