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A210507
Number of labeled graphs on [n] with unicyclic components containing a given edge.
0
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.
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
KEYWORD
nonn
AUTHOR
Gary Gordon, Jan 25 2013
STATUS
approved