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Find the generation funion of binary trees with nvertices and the number of binary trees with n vertices

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Exercice given at the end of Leure.

By definition, a finite tree t is binary if every vertex u ∈ t has either , or  children. Find the generation funion of binary trees with nvertices and the number of binary trees with n vertices.

Hint. Since there are no binary trees with an even number of vertices, it would perhaps be useful to consider inead binary trees withkleaves (a leaf being a vertex without a child).

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