|
| |
|
|
A006932
|
|
Number of permutations of [n] with at least one strong fixed point (a permutation p of {1,2,...,n} is said to have j as a strong fixed point if p(k)<j for k<j and p(k)>j for k>j).
(Formerly M2862)
|
|
4
| |
|
|
1, 1, 3, 10, 43, 223, 1364, 9643, 77545, 699954, 7013079, 77261803, 928420028, 12085410927, 169413357149, 2544367949634, 40758600588283, 693684669653911, 12499734669634036, 237734433597317987, 4759174459355303521
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,3
|
|
|
REFERENCES
| Problem E3467, Amer. Math. Monthly, 100 (1993), 800-801.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
Stanley, R. P., Enumerative Combinatorics, Volume 1 (1986), p. 49.
K. Wayland, personal communication.
|
|
|
LINKS
| V. Strehl, The average number of splitters in a random permutation [Unpublished; included here with the author's permission.]
|
|
|
MAPLE
| t1 := sum(n!*x^n, n=0..100): F := series(t1/(1+x*t1), x, 100): for i from 1 to 40 do printf(`%d, `, i!-coeff(F, x, i)) od:
|
|
|
MATHEMATICA
| m = 22; s = Sum[n!*x^n, {n, 0, m}]; Range[0, m-1]! - CoefficientList[Series[s/(1+x*s), {x, 0, m}], x][[1;; m]] // Rest (* From Jean-François Alcover, Apr 28 2011, after Maple code *)
|
|
|
CROSSREFS
| Cf. A052186.
Sequence in context: A030833 A157313 A030971 * A001040 A162286 A032269
Adjacent sequences: A006929 A006930 A006931 * A006933 A006934 A006935
|
|
|
KEYWORD
| nonn,easy,nice
|
|
|
AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
|
|
|
EXTENSIONS
| More terms and Maple code from James A. Sellers (sellersj(AT)math.psu.edu), Mar 13 2000
Edited by Emeric Deutsch, Oct 29 2008
|
| |
|
|
