Statements (34)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
integer sequence
|
| gptkbp:appearsIn |
gptkb:Pascal's_triangle
|
| gptkbp:application |
gptkb:probability_theory
combinatorics enumeration of Dyck paths lattice path counting |
| gptkbp:author |
gptkb:N._J._A._Sloane
|
| gptkbp:citation |
gptkb:A007318
A000108 A000984 |
| gptkbp:describes |
Central binomial coefficients: binomial(2n, n), n >= 0.
|
| gptkbp:first_terms |
2
1 20 252 6 70 924 3432 12870 48620 |
| gptkbp:form |
a(n) = binomial(2n, n)
|
| gptkbp:generatingFunction |
1/sqrt(1-4x)
|
| gptkbp:hasKeyword |
nonn, easy, nice
|
| https://www.w3.org/2000/01/rdf-schema#label |
A001157
|
| gptkbp:OEIS |
gptkb:A001157
https://oeis.org/A001157 |
| gptkbp:offset |
0
|
| gptkbp:recurrence |
a(n) = 2*(2n-1)*a(n-1)/n, a(0)=1
|
| gptkbp:relatedTo |
gptkb:Catalan_numbers
binomial coefficients |
| gptkbp:sequence |
gptkb:Central_binomial_coefficients
|
| gptkbp:bfsParent |
gptkb:A000203
|
| gptkbp:bfsLayer |
8
|