Catalan number

A kind of number

About Catalan number

Catalan numbers C_n = (2n choose n)/(n+1) count many combinatorial structures: binary trees, Dyck paths, non-crossing partitions, etc. The first few are 1, 2, 5, 14, 42, 132, 429.

Key features

  • Named after Eugène Charles Catalan.
  • C_0 = 1, C_1 = 1, C_2 = 2, C_3 = 5, C_4 = 14, C_5 = 42, ….

Examples:

1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796

Further reading