Statements (41)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
integer sequence
|
| gptkbp:application |
number of ways to choose n objects from 2n
number of monotonic lattice paths along the edges of a grid from (0,0) to (n,n) number of lattice paths from (0,0) to (n,n) without crossing the diagonal |
| gptkbp:author |
gptkb:N._J._A._Sloane
|
| gptkbp:citation |
gptkb:OEIS_A000984
gptkb:OEIS_A007318 gptkb:Concrete_Mathematics_by_Graham,_Knuth,_Patashnik gptkb:Handbook_of_Mathematical_Functions_by_Abramowitz_and_Stegun OEIS A002894 |
| gptkbp:describes |
Central binomial coefficients: C(2n, n) = (2n)!/(n!)^2
|
| gptkbp:first_terms |
2
1 20 252 6 70 924 3432 12870 48620 184756 |
| gptkbp:form |
a(n) = binomial(2n, n)
a(n) = (2n)!/(n!)^2 a(n) = Product_{k=1..n} (n+k)/k |
| gptkbp:generating_function |
1/sqrt(1-4x)
|
| gptkbp:hasKeyword |
easy
nice core full nonn fini |
| https://www.w3.org/2000/01/rdf-schema#label |
OEIS A001405
|
| gptkbp:name |
binomial coefficients (central)
|
| gptkbp:OEIS |
gptkb:A001405
|
| gptkbp:recurrence |
a(n) = 2*(2n-1)*a(n-1)/n, a(0)=1
|
| gptkbp:sequence |
combinatorial sequence
binomial coefficient |
| gptkbp:sequence_in_OEIS |
https://oeis.org/A001405
|
| gptkbp:bfsParent |
gptkb:OEIS_A000984
|
| gptkbp:bfsLayer |
8
|