|
| |
|
|
A007999
|
|
a(n)=number of permutations w of 1,2,...,n such that w and w^{-1} are alternating.
|
|
1
| |
|
|
1, 1, 2, 3, 8, 19, 64, 213, 880, 3717, 18288, 92935, 531440, 3147495, 20525168, 138638825, 1015694832, 7700244745, 62623847536, 526317901451, 4705365925872, 43407723925499, 423149546210416, 4250149857500861, 44868038386273776
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,3
|
|
|
REFERENCES
| Foulkes, H. O.; Tangent and secant numbers and representations of symmetric groups. Discrete Math. 15 (1976), no. 4, 311-324.
R. P. Stanley, Alternating permutations and symmetric functions, in preparation.
|
|
|
LINKS
| R. P. Stanley, Alternating permutations and symmetric functions [From Joel Brewster Lewis (jblewis(AT)post.harvard.edu), May 21 2009]
|
|
|
FORMULA
| sum_{n=0..infinity} a(n)x^n = sum_{k=0..infinity} E_{2k+1}^2 u^{2k+1}/(2k+1)! + (1-x^2)^{-1/2} sum_{k=0..infinity} E_{2k}^2 u^{2k}/(2k)!, where E_j is an Euler number and u = (1/2)log((1+x)/(1-x)). - R. P. Stanley (rstan(AT)math.mit.edu), Jan 21 2006
|
|
|
CROSSREFS
| Sequence in context: A148042 A077269 A148043 * A006609 A005663 A112834
Adjacent sequences: A007996 A007997 A007998 * A008000 A008001 A008002
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| poirier(AT)lacim.uqam.ca, Simon Plouffe (simon.plouffe(AT)gmail.com)
|
|
|
EXTENSIONS
| More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), May 15 2007
|
| |
|
|
