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a(9)=543 since we have several cases, with one unicyclic graph, or two, or three. Namely,
-One triangle and a forest of order 6, or 20 graphs.
-One unicyclic graph with 4 nodes and a forest of order 5, or 20 graphs.
-One unicyclic graph with 5 nodes and a forest of order 4, or 30 graphs.
-One unicyclic graph with 6 nodes and a forest of order 3, or 39 graphs.
-One unicyclic graph of 7 nodes and a forest of order 2, or 66 graphs.
-One unicyclic graph of 8 nodes and an isolated vertex, or 89 graphs.
-One unicyclic graph of 9 nodes, or 240 graphs.
-Two triangles and a forest of order 3, or 3 graphs.
-One triangle plus one unicyclic graph of 4 nodes plus a forest of order 2, or 4 graphs.
-One triangle plus one unicyclic graph of 5 nodes plus an isolated vertex, or 5 graphs.
-One triangle plus one unicyclic graph of 6 nodes, or 13 graphs.
-Two unicyclic graphs of 4 nodes and an isolated vertex, or C(2+2-1,2)=3 graphs.
-One unicyclic graph of 5 nodes, and another of 4 nodes, or 10 graphs.
-Three triangles, or 1 graph.
Total = 543.
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