A210507 Number of labeled graphs on [n] with unicyclic components containing a given edge.

1, 10, 111, 1468, 22940, 416250, 8626660, 201349672, 5230931454, 149783426470, 4688281021490, 159284662406460, 5838769123729984, 229711022253150382, 9655348958575618320, 431845990498159342000, 20479127764425617465660, 1026429489947790074019978

Offset

3,2

Comments

This gives the number of matroid bases that contain a given element (edge) of the bicircular matroid of K_n.

References

O. Giménez, A. de Mier, M. Noy, On the Number of Bases of Bicircular Matroids, Ann. Comb. 9 (2005), no. 1, 35-45.

Links

Table of n, a(n) for n=3..20.

Formula

a(n) = 2*b(n)/(n-1), where b(n) is seq A137916.

Example

a(4)=10 means that 10 (of the 15) labeled unicyclic graphs on 4 vertices contain a given edge.

Crossrefs

Cf. A137916.

Sequence in context: A122574 A176736 A084031 * A066275 A362671 A344398

Adjacent sequences: A210504 A210505 A210506 * A210508 A210509 A210510

Keyword

nonn

Author

Gary Gordon, Jan 25 2013

Status

approved