|
| |
|
|
A001267
|
|
One-half the number of permutations of length n with exactly 3 rising or falling successions.
(Formerly M4550 N1934)
|
|
7
| |
|
|
0, 0, 0, 0, 1, 8, 60, 444, 3599, 32484, 325322, 3582600, 43029621, 559774736, 7841128936, 117668021988, 1883347579515, 32026067455084, 576605574327174, 10957672400252944, 219190037987444577, 4603645435776504120, 101292568208941883236, 2329975164242735146316
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,6
|
|
|
COMMENTS
| (1/2) times number of permutations of 12...n such that exactly 3 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.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
|
|
|
FORMULA
| Coefficient of t^3 in S[n](t) defined in A002464, divided by 2.
|
|
|
CROSSREFS
| Cf. A002464, A000130, A086852. Equals A086854/2. A diagonal of A010028.
Sequence in context: A093132 A094169 A129325 * A099156 A199526 A129331
Adjacent sequences: A001264 A001265 A001266 * A001268 A001269 A001270
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
|
| |
|
|
