CatalanNumber

The nth Catalan number , counting balanced bracket sequences, binary trees, polygon triangulations, and many other structures of size n.

WikipediaCatalan number↗MathWorldCatalanNumber↗WikidataQ270513↗nLabCatalan number↗DLMF26.5.E1↗OEISA000108↗Wolfram LanguageCatalanNumber!↗

CatalanNumber(n)the nth Catalan number .

SageMathcatalan_number(n)↗SymPycatalan(n)↗

Domain: Combinatorics

Details

• The Catalan numbers have the closed form .
• They satisfy the recurrence with .
• is the number of monotonic lattice paths from one corner of an grid to the opposite corner that stay below the diagonal.
• compute-engine defines on nonnegative integers; extension to real and complex arguments through the Binomial gamma-function form is not yet supported.

Examples

See also: Binomial, BellNumber