|
| |
|
|
A113897
|
|
Triangle read by rows: number of simsun n-permutations with k descents.
|
|
0
| |
|
|
1, 1, 1, 1, 4, 1, 11, 4, 1, 26, 34, 1, 57, 180, 34, 1, 120, 768, 496, 1, 247, 2904, 4288, 496, 1, 502, 10194, 28768, 11056, 1, 1013, 34096, 166042, 141584, 11056, 1, 2036, 110392, 868744, 1372088, 349504, 1, 4083, 349500, 4247720, 11204160, 6213288, 349504
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,5
|
|
|
COMMENTS
| Is this A094503 after removal of the top row? [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 13 2008]
|
|
|
REFERENCES
| R. P. Stanley, Flag f-vectors and the cd-index, Math. Zeitschrift 216 (1994), 483-499.
S. Sundaram, Plethysm, Partitions with an Even Number of Blocks and Euler Numbers in "Formal Power Series and Algebraic Combinatorics 1994," DIMACS Series in Discrete Mathematics and Theoretical Computer Science 24, AMS (1996).
|
|
|
FORMULA
| ss(n, k)=(k+1)ss(n-1, k)+(n-2k+1)ss(n-1, k-1); ss(n, t):=Sum_{k=0..floor(n/2)}ss(n, k)t^k, ss(n, t)=((n-1)t+1)ss(n-1, t)+t(1-2t)ss(n-1, t)'. e.g.f. = (2t-1)(sec(x*sqrt(2t-1)/2)/(sqrt(2t-1)-tan(x*sqrt(2t-1)/2)))^2.
|
|
|
EXAMPLE
| 1; 1, 1; 1, 4; 1, 11, 4; 1, 26, 34; 1, 57, 180, 34; ...
|
|
|
CROSSREFS
| Cf. A000111, A000295, A002105.
Sequence in context: A124324 A178519 A094503 * A158753 A183884 A135552
Adjacent sequences: A113894 A113895 A113896 * A113898 A113899 A113900
|
|
|
KEYWORD
| easy,nonn
|
|
|
AUTHOR
| Chak-On Chow (cchow(AT)alum.mit.edu), Jan 28 2006
|
|
|
EXTENSIONS
| Corrected and extended by Vladeta Jovovic (vladeta(AT)eunet.rs), Jan 30 2006
|
| |
|
|
