Statements (29)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
integer sequence
|
| gptkbp:author |
gptkb:N._J._A._Sloane
|
| gptkbp:citation |
gptkb:OEIS_A000108
gptkb:OEIS_A000984 gptkb:OEIS_A007318 OEIS A002457 |
| gptkbp:describes |
Central binomial coefficients: binomial(2n, n).
|
| gptkbp:first_terms |
1, 2, 6, 20, 70, 252, 924, 3432, 12870, 48620, 184756, 705432, 2704156, 10400600, 40116600, 155117520, 601080390, 2333606220, 9075135300, 35345263800
|
| gptkbp:form |
a(n) = (2n)! / (n!)^2
a(n) = binomial(2n, n) |
| gptkbp:hasCombinatorialInterpretation |
Number of ways to arrange n pairs of parentheses.
Number of lattice paths from (0,0) to (n,n) with steps (1,0) and (0,1). Number of ways to choose n objects from 2n objects. |
| gptkbp:hasGeneratingFunction |
1/sqrt(1-4x)
|
| gptkbp:hasKeyword |
easy
nice core full nonn fini |
| gptkbp:hasOEISId |
A001700
|
| https://www.w3.org/2000/01/rdf-schema#label |
OEIS A001700
|
| gptkbp:OEIS |
true
|
| gptkbp:offset |
0,2
|
| gptkbp:relatedTo |
gptkb:Catalan_numbers
|
| gptkbp:sequence |
gptkb:Central_binomial_coefficients
binomial coefficient |
| gptkbp:bfsParent |
gptkb:OEIS_A003215
|
| gptkbp:bfsLayer |
8
|