Definition
Catalan numbers
Also known as: catalan sequence
A famous sequence of whole numbers — 1, 1, 2, 5, 14, 42 and so on — that counts a surprising range of balanced or recursive structures. They appear in coin-flip and ballot problems, for instance counting paths of heads and tails that never let one side fall behind the other. They turn up naturally in random walks and in many counting puzzles across combinatorics.