Catalan sequence

The Catalan Numbers are a sequence of numbers that show up in a variety of instances.

Introduction

Catalan numbers can be used to find:

The number of ways to arrange $n$ pairs of matching parentheses
The number of ways a convex polygon of $n+2$ sides can be split into $n$ triangles
The number of rooted binary trees with exactly $n+1$ leaves

Example

In how many ways can the product of $n$ ordered number be calculated by pairs? For example, the possible ways for $a\cdot b\cdot c\cdot d$ are $a((bc)d), a(b(cd)), (ab)(cd), ((ab)c)d,$ and $(a(bc))d$ .

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Catalan sequence

Contents

Introduction

Example

Solution

See also