Statements (34)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
integer sequence
|
| gptkbp:alsoKnownAs |
gptkb:Schröder_numbers
|
| gptkbp:application |
counting plane trees
enumeration of certain lattice paths parenthesizations of products |
| gptkbp:combinatorialInterpretation |
number of ways to insert parentheses in a sequence of n+1 factors
number of lattice paths from (0,0) to (n,n) using steps (1,0), (0,1), (1,1) that never rise above the line y=x |
| gptkbp:field |
combinatorics
|
| gptkbp:first_terms |
2
1 1806 22 6 90 394 1037718 140130594 206098 41586 5285214 726915254 8558 27166938 3802843966 |
| gptkbp:generatingFunction |
(1-x-sqrt(1-6x+x^2))/(2x)
|
| gptkbp:growthForm |
asymptotically 4^n
|
| https://www.w3.org/2000/01/rdf-schema#label |
large 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), S(0)=1
|
| gptkbp:relatedTo |
gptkb:Catalan_numbers
small Schröder numbers |
| gptkbp:bfsParent |
gptkb:Schröder–Hipparchus_numbers
|
| gptkbp:bfsLayer |
7
|