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A145903
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Generalised Narayana numbers for root systems of type D_n. Triangle of h-vectors of type D associahedra.
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3
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1, 1, 1, 1, 2, 1, 1, 6, 6, 1, 1, 12, 24, 12, 1, 1, 20, 70, 70, 20, 1, 1, 30, 165, 280, 165, 30, 1, 1, 42, 336, 875, 875, 336, 42, 1, 1, 56, 616, 2296, 3500, 2296, 616, 56, 1, 1, 72, 1044, 5292, 11466, 11466, 5292, 1044, 72, 1
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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COMMENTS
| The generalised Narayana numbers of type D_n (row n of this triangle) are defined as the entries of the h-vector of the simplicial complex dual to the generalised associahedron of type D_n [Fomin & Reading, p.60]. For the corresponding triangle of f-vectors see A080721. For Narayana numbers of root systems of type A and type B see A001263 and A008459 respectively.
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LINKS
| S. Fomin, N. Reading, Root systems and generalized associahedra, Lecture notes for IAS/Park-City 2004.
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FORMULA
| For n >= 2, T(n,k) = binomial(n,k)^2 - n/(n-1)*binomial(n-1,k-1)*binomial(n-1,k).
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EXAMPLE
| Root systems of type D_n are defined only for n >= 2. It seems
convenient to complete the array to form a lower unit triangular matrix.
Triangle starts
n\k|..0....1....2....3....4....5....6
=====================================
0..|..1
1..|..1....1
2..|..1....2....1
3..|..1....6....6....1
4..|..1...12...24...12....1
5..|..1...20...70...70...20....1
6..|..1...30..165..280..165...30....1
...
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CROSSREFS
| A001263, A008459, A051924 (row sums), A080721.
Sequence in context: A157635 A075798 A155864 * A173881 A172373 A174411
Adjacent sequences: A145900 A145901 A145902 * A145904 A145905 A145906
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KEYWORD
| easy,nonn,tabl
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AUTHOR
| Peter Bala (pbala(AT)toucansurf.com), Oct 28 2008
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