Vamsi Nonisomorphic Homeomorphic Irreducible Trees

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Vamsi paused while watching the movie Goodwill Hunting and felt that the problem solved by Matt Damon was an easy one. "How many non-isomorphic homeomorphically irreducible trees are there on 10 vertices?" He extended it for N vertices. Alas! he couldn't figure a pattern out. Doing so he stumbles upon something interesting. He begins enumerating number of trees with vertices D, where each node (wh

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