Catalan Numbers
Ballot sequences · Triangulations · Dyck paths · Mountain ranges
n =
6
C(
6
) =
132
Visualization
Dyck Paths
Mountains
Triangulations
Ballot
← Previous
Next →
Auto-cycle
Formula:
C(n) = (2n)! / ((n+1)! · n!)
Sequence:
1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862…
Dyck paths:
lattice paths from (0,0) to (2n,0) using +1/−1 steps, never going negative.