|
| |
|
|
A086856
|
|
Triangle read by rows: T(n,k) = one-half number of permutations of length n with exactly k rising or falling successions, for n >= 1, 0 <= k <= n-1. T(1,0) = 1 by convention.
|
|
2
| |
|
|
1, 0, 1, 0, 2, 1, 1, 5, 5, 1, 7, 20, 24, 8, 1, 45, 115, 128, 60, 11, 1, 323, 790, 835, 444, 113, 14, 1, 2621, 6217, 6423, 3599, 1099, 183, 17, 1, 23811, 55160, 56410, 32484, 11060, 2224, 270, 20, 1, 239653, 545135, 554306, 325322, 118484, 27152, 3950, 374, 23, 1, 2648395
(list; table; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,5
|
|
|
COMMENTS
| (1/2) times number of permutations of 12...n such that exactly k of the following occur: 12, 23, ..., (n-1)n, 21, 32, ..., n(n-1).
|
|
|
REFERENCES
| F. N. David, M. G. Kendall and D. E. Barton, Symmetric Function and Allied Tables, Cambridge, 1966, p. 263.
J. Riordan, A recurrence for permutations without rising or falling successions. Ann. Math. Statist. 36 (1965), 708-710.
|
|
|
EXAMPLE
| 1; 0,1; 0,2,1; 1,5,5,1; 7,20,24,8,1; ...
|
|
|
CROSSREFS
| Diagonals give A001266 (and A002464), A000130, A000349, A001267, A001268.
Triangle in A001100 divided by 2. A010028 transposed.
Sequence in context: A091378 A156045 A119687 * A052916 A156576 A176093
Adjacent sequences: A086853 A086854 A086855 * A086857 A086858 A086859
|
|
|
KEYWORD
| tabl,nonn
|
|
|
AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Aug 19 2003
|
| |
|
|
