|
Search: id:A097971
|
|
|
| A097971 |
|
Number of alternating runs in all permutations of [n] (the permutation 732569148 has four alternating runs: 732, 2569, 91 and 148). |
|
+0
2
|
|
| 2, 10, 56, 360, 2640, 21840, 201600, 2056320, 22982400, 279417600, 3672345600, 51891840000, 784604620800, 12640852224000, 216202162176000, 3912561709056000, 74694359900160000, 1500289571708928000
(list; graph; listen)
|
|
|
OFFSET
|
2,1
|
|
|
REFERENCES
|
M. Bona, Combinatorics of Permutations, Chapman & Hall/CRC, Boca Raton, FL, 2004, pp. 24-30.
D. E. Knuth, The Art of Computer Programming. Addison-Wesley, Reading, MA, 1973, Vol. 3, pp. 46 and 587-8.
|
|
FORMULA
|
a(n)=n!(2n-1)/3. E.g.f. = x^2*(3-x)/[3(1-x)^2]. a(n)=2*A006157
|
|
EXAMPLE
|
a(3)=10 because the permutations 123, 132, 312, 213, 231, 321 have the following alternating runs: 123, 13, 32, 31, 12, 21, 13, 23, 31 and 321.
|
|
MAPLE
|
seq(n!*(2*n-1)/3, n=2..20);
|
|
CROSSREFS
|
Cf. A006157.
Adjacent sequences: A097968 A097969 A097970 this_sequence A097972 A097973 A097974
Sequence in context: A108490 A165817 A000172 this_sequence A093303 A075870 A074608
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Emeric Deutsch and Ira Gessel (deutsch(AT)duke.poly.edu), Sep 07 2004
|
|
|
Search completed in 0.002 seconds
|
