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A210507 Number of labeled graphs on [n] with unicyclic components containing a given edge. 0

%I

%S 1,10,111,1468,22940,416250,8626660,201349672,5230931454,149783426470,

%T 4688281021490,159284662406460,5838769123729984,229711022253150382,

%U 9655348958575618320,431845990498159342000,20479127764425617465660,1026429489947790074019978

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

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

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

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

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

%Y Cf. A137916.

%K nonn

%O 3,2

%A _Gary Gordon_, Jan 25 2013

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Last modified October 16 21:10 EDT 2019. Contains 328103 sequences. (Running on oeis4.)