Central binomial coefficients
GPTKB entity
Statements (24)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:application |
gptkb:Probability_theory
gptkb:Catalan_numbers Counting lattice paths |
| gptkbp:asymptotic |
C(2n, n) ~ 4^n / sqrt(pi n)
|
| gptkbp:author |
Isaac Newton (binomial theorem)
|
| gptkbp:defines |
The binomial coefficient C(2n, n) for n ≥ 0
|
| gptkbp:field |
Combinatorics
|
| gptkbp:first_terms |
1
|
| gptkbp:form |
C(2n, n)
|
| gptkbp:generating_function |
1/sqrt(1-4x)
|
| https://www.w3.org/2000/01/rdf-schema#label |
Central binomial coefficients
|
| gptkbp:OEIS |
A000984
|
| gptkbp:property |
Always integer
Largest binomial coefficient for given 2n Symmetric in n |
| gptkbp:recurrence |
C(2n+2, n+1) = 2(2n+1)/(n+1) * C(2n, n)
|
| gptkbp:relatedTo |
gptkb:Catalan_numbers
Binomial coefficients |
| gptkbp:sequence |
1, 2, 6, 20, 70, 252, 924, ...
|
| gptkbp:bfsParent |
gptkb:A001003
gptkb:OEIS_A000984 gptkb:A001097_(OEIS) |
| gptkbp:bfsLayer |
8
|