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How many trees T are there on the set of vertices {1, 2, 3, 4, 5,...

How many trees T are there on the set of vertices
{1, 2, 3, 4, 5, 6, 7} in which the vertices 2 and 3 have degree 3, vertex
5 has degree 2, and hence all others have degree 1? Do not just
draw pictures but consider the possible Pr¨ufer codes of these trees.

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