Statements (32)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
integer sequence
|
| gptkbp:alsoKnownAs |
gptkb:Schröder_number
|
| gptkbp:appearsIn |
combinatorics
|
| gptkbp:describes |
number of lattice paths from (0,0) to (n,n) with steps (1,0), (0,1), (1,1) that do not rise above the line y=x
|
| gptkbp:first_terms |
2
1 1806 22 6 90 394 1037718 140130594 206098 27183006 41586 5285214 8558 19835652834 3789641262 726082564 |
| https://www.w3.org/2000/01/rdf-schema#label |
large Schröder number
|
| gptkbp:namedAfter |
gptkb:Ernst_Schröder
|
| gptkbp:OEIS |
gptkb:A006318
|
| gptkbp:recurrence |
S(n) = S(0)S(n-1) + S(1)S(n-2) + ... + S(n-1)S(0) + S(n-1), S(0)=1
|
| gptkbp:relatedTo |
gptkb:Catalan_number
gptkb:small_Schröder_number |
| gptkbp:usedFor |
counting certain lattice paths
counting non-crossing partitions counting plane trees |
| gptkbp:bfsParent |
gptkb:Schröder's_number
|
| gptkbp:bfsLayer |
7
|