Statements (30)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:integer_sequence
|
| gptkbp:alsoKnownAs |
central binomial coefficients
|
| gptkbp:appearsIn |
gptkb:combinatorics
gptkb:algebra gptkb:probability_theory |
| gptkbp:author |
gptkb:N._J._A._Sloane
|
| gptkbp:combinatorialInterpretation |
number of ways to choose n objects from 2n objects
number of lattice paths from (0,0) to (n,n) not rising above the line y=x |
| gptkbp:definedIn |
C(2n, n)
|
| gptkbp:first_terms |
2
1 20 252 6 70 924 3432 12870 48620 |
| gptkbp:form |
C(2n, n) = (2n)! / (n!)^2
|
| gptkbp:generatingFunction |
1/sqrt(1-4x)
|
| gptkbp:OEIS |
https://oeis.org/A002117
|
| gptkbp:OEISNumber |
gptkb:A002117
|
| gptkbp:recurrence |
a(n) = 2*(2n-1)*a(n-1)/n, a(0)=1
|
| gptkbp:relatedTo |
gptkb:Catalan_numbers
binomial coefficients |
| gptkbp:sequence |
non-negative integers
|
| gptkbp:bfsParent |
gptkb:Apéry's_constant
|
| gptkbp:bfsLayer |
6
|
| https://www.w3.org/2000/01/rdf-schema#label |
A002117
|