Statements (27)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
integer sequence
|
| gptkbp:alsoKnownAs |
gptkb:large_Schröder_numbers
|
| gptkbp:field |
combinatorics
|
| gptkbp:first_terms |
1
11 197 3 45 903 103049 20793 2646723 4279 518859 |
| gptkbp:form |
S(n) = sum_{k=0}^{n-1} S(k) * S(n-1-k) + 2 * sum_{k=1}^{n-1} S(k) * S(n-k) for n > 0, S(0) = 1
|
| https://www.w3.org/2000/01/rdf-schema#label |
Schröder–Hipparchus numbers
|
| gptkbp:namedAfter |
gptkb:Ernst_Schröder
gptkb:Hipparchus |
| gptkbp:numberOfRooms |
number of plane trees with n+1 leaves
number of ways to insert parentheses in a sequence of n+1 factors number of ways to divide a convex polygon into n+1 regions by non-crossing diagonals |
| gptkbp:OEIS |
gptkb:A001003
|
| gptkbp:relatedTo |
gptkb:Catalan_numbers
gptkb:Schröder_numbers |
| gptkbp:sequence |
non-negative integer sequence
|
| gptkbp:bfsParent |
gptkb:Ernst_Schröder
|
| gptkbp:bfsLayer |
6
|