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A113897 Triangle read by rows: number of simsun n-permutations with k descents. 1
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; text; internal format)
OFFSET

1,5

COMMENTS

Is this A094503 after removal of the top row? [From R. J. Mathar, 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).

LINKS

Table of n, a(n) for n=1..48.

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,tabf

AUTHOR

Chak-On Chow (cchow(AT)alum.mit.edu), Jan 28 2006

EXTENSIONS

Corrected and extended by Vladeta Jovovic, Jan 30 2006

STATUS

approved

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Last modified February 24 20:33 EST 2020. Contains 332210 sequences. (Running on oeis4.)