Statements (29)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
integer sequence
|
| gptkbp:application |
combinatorics
plane trees counting lattice paths parenthesizations |
| gptkbp:first_terms |
2
1 1806 22 6 90 394 206098 41586 8558 1, 2, 6, 22, 90, 394, 1806, 8558, 41586, 206098 |
| gptkbp:form |
S(n) = sum_{k=0}^{n-1} S(k) * S(n-1-k) + S(n-1)
|
| gptkbp:growthForm |
exponential
|
| https://www.w3.org/2000/01/rdf-schema#label |
Schröder numbers
|
| gptkbp:namedAfter |
gptkb:Ernst_Schröder
|
| gptkbp:OEIS |
gptkb:A006318
|
| gptkbp:recurrence |
S(n) = S(n-1) + sum_{k=1}^{n-1} S(k) * S(n-k) for n > 0, S(0) = 1
|
| gptkbp:relatedTo |
gptkb:Catalan_numbers
gptkb:large_Schröder_numbers small Schröder numbers |
| gptkbp:sequence |
non-negative integers
|
| gptkbp:bfsParent |
gptkb:Catalan_numbers
gptkb:Schröder–Hipparchus_numbers |
| gptkbp:bfsLayer |
7
|