|
Search: id:A000349
|
|
|
| A000349 |
|
One-half the number of permutations of length n with exactly 2 rising or falling successions.
(Formerly M3932 N1617)
|
|
+0
9
|
|
| 0, 0, 0, 1, 5, 24, 128, 835, 6423, 56410, 554306, 6016077, 71426225, 920484892, 12793635300, 190730117959, 3035659077083, 51371100102990, 920989078354838, 17437084517068465, 347647092476801301, 7280060180210901232, 159755491837445900120, 3665942433747225901707
(list; graph; listen)
|
|
|
OFFSET
|
0,5
|
|
|
COMMENT
|
(1/2) times number of permutations of 12...n such that exactly 2 of the following occur: 12, 23, ..., (n-1)n, 21, 32, ..., n(n-1).
|
|
REFERENCES
|
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
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.
|
|
FORMULA
|
Coefficient of t^2 in S[n](t) defined in A002464, divided by 2.
|
|
CROSSREFS
|
Cf. A002464, A000130, A086852. Equals A086853/2. A diagonal of A010028.
Sequence in context: A055825 A006326 A058120 this_sequence A036919 A020067 A066118
Adjacent sequences: A000346 A000347 A000348 this_sequence A000350 A000351 A000352
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
N. J. A. Sloane (njas(AT)research.att.com).
|
|
|
Search completed in 0.002 seconds
|
