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

0,3

Comments

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

Links

Table of n, a(n) for n=0..20.

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

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]

Crossrefs

Sequence in context: A222081 A047735 A096364 * A049119 A367423 A332236

Adjacent sequences: A210658 A210659 A210660 * A210662 A210663 A210664

Keyword

nonn

Author

Geoffrey Critzer, Mar 30 2012

Status

approved