A210661 The total number of ways to linearly order the connected components of each functional digraph over all functions f:{1,2,...,n}->{1,2,...,n}.

1, 1, 5, 41, 464, 6679, 116534, 2387223, 56126216, 1488936405, 43981641232, 1431351648253, 50877935705904, 1960987188622955, 81454893191133968, 3627186997857749259, 172364960657294194944, 8705953783492490785801, 465732966748611591349632, 26305402198153236286685809, 1564288763576093814775234304

Offset: 0

Author

Geoffrey Critzer, Mar 30 2012

Keywords

• nonn

Comments

Sum_{k=1,2,...,n}:A060281(n,k)*k!

Programs

Mathematica

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

Formula

E.g.f.: 1/(1-log(1/(1-T(x)))) where T(x) is the e.g.f. for A000169.

a(n) ~ n! * exp((2*n*exp(1)-exp(1)-n)*exp(-1))/(exp(1)-1)^(n+1). - Vaclav Kotesovec, Sep 24 2013