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Search: id:A066094
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| A066094 |
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Type D Eulerian triangle. |
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+0
7
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| 1, 1, 1, 1, 2, 1, 1, 11, 11, 1, 1, 44, 102, 44, 1, 1, 157, 802, 802, 157, 1, 1, 530, 5551, 10876, 5551, 530, 1, 1, 1731, 35121, 124427, 124427, 35121, 1731, 1, 1, 5528, 208732, 1265704, 2201030, 1265704, 208732, 5528, 1
(list; table; graph; listen)
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OFFSET
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0,5
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COMMENT
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Let n >= 2, and write the polynomial D(n,0)+D(n,1)*x+...+D(n,n)*x^n as a polynomial in y := x-1. Then the coefficient of y^r is the number of cells of dimension n-r in the cellular decomposition of a Euclidean space containing a root system of type D_n. If n >= 2 then the corresponding row sum is 2^(n-1)*(n-1)!, while sum(2^k*D(n,k),k=0..n) is given by sequence A080254.
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REFERENCES
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K. S. Brown, Buildings, Springer-Verlag, 1988
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LINKS
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C. Chow, On the Eulerian polynomials of type D.
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FORMULA
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Let D(n, k) denote the (k+1)st entry in the (n+1)st row, and let A(n, k), B(n, k) be triangles A008292 (The Eulerian triangle), A060187 respectively. Then D(n, k)=B(n, k)-2^(n-1)*n*A(n-2, k-1).
Chow gives complicated recurrences and generating functions.
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CROSSREFS
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Cf. A008292, A060187, A080254.
Sequence in context: A104251 A064307 A110905 this_sequence A010246 A054505 A132610
Adjacent sequences: A066091 A066092 A066093 this_sequence A066095 A066096 A066097
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KEYWORD
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easy,nonn,tabl
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AUTHOR
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Paul Boddington (psb(AT)maths.warwick.ac.uk), Mar 05 2003
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