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

Author

Gary Gordon, Jan 25 2013

Keywords

• nonn

Comments

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

Examples

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

References

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

Crossrefs

Cf. A137916.

Formula

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