Statements (32)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
integer sequence
|
| gptkbp:alsoKnownAs |
gptkb:large_Schröder_number
|
| gptkbp:application |
enumerative combinatorics
|
| gptkbp:field |
gptkb:mathematics
|
| gptkbp:first_terms |
2
1 1806 22 6 90 394 1037718 140130594 206098 27183006 3807564922 41586 5285214 726915254 8558 |
| gptkbp:generatingFunction |
(1 - x - sqrt(1 - 6x + x^2)) / (2x)
|
| https://www.w3.org/2000/01/rdf-schema#label |
Schröder's number
|
| gptkbp:namedAfter |
gptkb:Ernst_Schröder
|
| gptkbp:numberOfRooms |
number of lattice paths from (0,0) to (n,n) not rising above the line y=x and using steps (1,0), (0,1), and (1,1)
number of ways to insert parentheses in a sequence of n+1 factors |
| gptkbp:OEIS |
gptkb:A006318
|
| gptkbp:recurrence |
S(0) = 1, S(n) = S(n-1) + sum_{k=1}^{n-1} S(k) * S(n-k) for n > 0
|
| gptkbp:relatedTo |
gptkb:Catalan_number
gptkb:little_Schröder_number |
| gptkbp:sequence |
combinatorial sequence
|
| gptkbp:bfsParent |
gptkb:Ernst_Schröder
|
| gptkbp:bfsLayer |
6
|