Howang
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Hi,
Please I need you help to solve this problem:
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Consider a planar tree with $n$ non-root vertices (root edge selected).
1. Give a generating function for vertices distance $d$ from the root.
2. Proof that the total number is $$\displaystyle \binom{2n}{n-d}\frac{2d+1}{(n+d+1)}$$
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We are supposed to have an exponential generating function then use Lagrange Inversion Theorem.
Please I need you help to solve this problem:
----------
Consider a planar tree with $n$ non-root vertices (root edge selected).
1. Give a generating function for vertices distance $d$ from the root.
2. Proof that the total number is $$\displaystyle \binom{2n}{n-d}\frac{2d+1}{(n+d+1)}$$
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We are supposed to have an exponential generating function then use Lagrange Inversion Theorem.