March 30 exercise (a) from lecture

Exercise: Complete part (a) below for your team.

Team parentheses:
Let $C_n$ be the number of ways of parenthesizing a product of $n+1$ numbers.

Team binary rooted trees:
Let $C_n$ be the number of full, binary, rooted trees with $n+1$ leaves.

Team triangulated polygons:
Let $C_n$ be the number of ways of triangulating a polygon with $n+2$ sides.

(a) Find $C_n$ for $n=0, 1, 2, 3, 4$.

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