grandes-ecoles 2021 Q9

grandes-ecoles · France · centrale-maths1__mp Permutations & Arrangements Combinatorial Proof or Identity Derivation

For every integer $n \geqslant 1$, we denote $C_{n}$ the number of well-parenthesized words of length $2n$. We set by convention $C_{0} = 1$.
By enumerating the different well-parenthesized words of length 2, 4 and 6, show that $C_{1} = 1$, $C_{2} = 2$ and determine $C_{3}$.

For every integer $n \geqslant 1$, we denote $C_{n}$ the number of well-parenthesized words of length $2n$. We set by convention $C_{0} = 1$.

By enumerating the different well-parenthesized words of length 2, 4 and 6, show that $C_{1} = 1$, $C_{2} = 2$ and determine $C_{3}$.

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