A200248 The number of (simultaneously) fixed and isolated points in the digraph representation of all functions f:{1,2,...,n}->{1,2,...,n}.

0, 1, 2, 9, 68, 710, 9414, 151032, 2840648, 61247664, 1488691530, 40262372480, 1199047315212, 38984874829056, 1373954963380622, 52171222364513280, 2123286652815757200, 92201888436661409792, 4255016114128163220882, 207954945060162884960256

Offset: 0

Author

Geoffrey Critzer, Nov 16 2011

Keywords

• nonn

Comments

A fixed point is a vertex with a self loop. An isolated point is a vertex that is not joined to any other vertex.

Links

• T. D. Noe, Table of n, a(n) for n = 0..101

Programs

Mathematica

t=Sum[n^(n-1)x^n/n!,{n,1,20}];Range[0,20]! CoefficientList[Series[x(Log[1/(1-t)]+1),{x,0,20}],x]

Formula

a(n)= n*A001865

E.g.f.: x*C(x) where C(x) is the e.g.f. for A001865