Statements (16)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
integer sequence
|
| gptkbp:appearsIn |
enumerative combinatorics
|
| gptkbp:category |
permutation statistics
|
| gptkbp:describes |
number of permutations of the numbers 1 to n with exactly k ascents
|
| gptkbp:first_terms |
1, 1 1, 1 4 1, 1 11 11 1, 1 26 66 26 1
|
| https://www.w3.org/2000/01/rdf-schema#label |
Eulerian numbers
|
| gptkbp:namedAfter |
gptkb:Leonhard_Euler
|
| gptkbp:notation |
A(n, k)
|
| gptkbp:OEIS |
gptkb:A008292
|
| gptkbp:recurrence |
A(n, k) = (n-k)A(n-1, k-1) + (k+1)A(n-1, k)
|
| gptkbp:relatedTo |
gptkb:Stirling_numbers
binomial coefficients |
| gptkbp:usedFor |
counting permutations by number of ascents
|
| gptkbp:usedIn |
combinatorics
|
| gptkbp:bfsParent |
gptkb:A008404
|
| gptkbp:bfsLayer |
7
|