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Search: id:A113897
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| A113897 |
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Triangle read by rows: number of simsun n-permutations with k descents. |
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+0
1
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| 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; listen)
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OFFSET
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1,5
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COMMENT
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Is this A094503 after removal of the top row? [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 13 2008]
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REFERENCES
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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).
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FORMULA
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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.
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EXAMPLE
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1; 1, 1; 1, 4; 1, 11, 4; 1, 26, 34; 1, 57, 180, 34; ...
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CROSSREFS
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Cf. A000111, A000295, A002105.
Sequence in context: A111964 A124324 A094503 this_sequence A158753 A135552 A109088
Adjacent sequences: A113894 A113895 A113896 this_sequence A113898 A113899 A113900
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KEYWORD
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easy,nonn
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AUTHOR
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Chak-On Chow (cchow(AT)alum.mit.edu), Jan 28 2006
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EXTENSIONS
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Corrected and extended by Vladeta Jovovic (vladeta(AT)eunet.rs), Jan 30 2006
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