Statements (19)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
integer sequence
|
| gptkbp:application |
counting Dyck paths
counting binary trees counting non-crossing partitions counting valid parenthesis expressions triangulations of polygons |
| gptkbp:category |
enumerative combinatorics
|
| gptkbp:field |
gptkb:mathematics
|
| gptkbp:first_terms |
1
|
| gptkbp:form |
C_n = (2n)! / ((n+1)! n!)
|
| https://www.w3.org/2000/01/rdf-schema#label |
Catalan number
|
| gptkbp:namedAfter |
gptkb:Eugène_Charles_Catalan
|
| gptkbp:OEIS |
A000108
|
| gptkbp:recurrence |
C_0 = 1, C_{n+1} = sum_{i=0}^n C_i C_{n-i}
|
| gptkbp:sequence |
1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, ...
|
| gptkbp:usedIn |
combinatorics
|
| gptkbp:bfsParent |
gptkb:Motzkin_number
gptkb:Schröder's_number |
| gptkbp:bfsLayer |
7
|