Statements (52)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
mathematical sequence
|
| gptkbp:application |
physics
computer science mathematics bioinformatics |
| gptkbp:characteristics |
C(n) is always a positive integer
C(n) can be computed in O(n) time C(n) grows exponentially C(n) is symmetric |
| gptkbp:defines |
C(n) = (2n)! / ((n + 1)!n!)
|
| gptkbp:electionYear |
14
42 |
| gptkbp:expansion |
C(n) ~ (4^n) / (n^(3/2)√π)
|
| gptkbp:firstSeason |
1
|
| gptkbp:generator |
C(x)_=_(1_-_√(1_-_4x))_/_(2x)
|
| gptkbp:hasPatentNumber |
gptkb:Cayley_numbers
Fibonacci numbers Dyck paths Eulerian numbers Motzkin numbers Tetrahedral numbers Non-crossing handshakes Non-crossing partitions Non-empty binary trees Paths in a grid Planar graphs Rooted trees Triangulations of convex polygons Valid parentheses combinations Ways to arrange parentheses Ways to connect points without crossing Ways to form binary search trees Stirling_numbers Bell_numbers Delaunay_triangulations Lah_numbers Triangular_numbers |
| https://www.w3.org/2000/01/rdf-schema#label |
Catalan numbers
|
| gptkbp:namedAfter |
gptkb:Eugène_Charles_Catalan
|
| gptkbp:ninthClaim |
1430
132 429 4862 |
| gptkbp:relatedTo |
combinatorial mathematics
|
| gptkbp:sequel |
2
1 5 |
| gptkbp:series |
C(n) = Σ C(i)C(n-i-1) for i=0 to n-1
|
| gptkbp:usedIn |
binary tree structures
counting paths in a grid parentheses matching polygon_triangulation |