Question: Draw all rooted (labelled) trees on 1, 2 and 3 vertices and find the number of rooted trees in each case. Can you guess at

Draw all rooted (labelled) trees on 1, 2 and 3 vertices and find the number of rooted trees in each
case. Can you guess at a general formula for the number of such trees on n vertices, where n is
a positive integer?

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