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A145903 Generalized Narayana numbers for root systems of type D_n. Triangle of h-vectors of type D associahedra.

%I A145903 #9 Dec 18 2015 11:55:07
%S A145903 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,
%T A145903 1,1,42,336,875,875,336,42,1,1,56,616,2296,3500,2296,616,56,1,1,72,
%U A145903 1044,5292,11466,11466,5292,1044,72,1
%N A145903 Generalized Narayana numbers for root systems of type D_n. Triangle of h-vectors of type D associahedra.
%C A145903 The generalized 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 generalized 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.
%D A145903 T. K. Petersen, Eulerian Numbers, Birkhauser, 2015, Chapter 12.
%H A145903 S. Fomin, N. Reading, <a href="http://arxiv.org/abs/math.CO/0505518">Root systems and generalized associahedra</a>, Lecture notes for IAS/Park-City 2004, arXiv:math/0505518 [math.CO], 2005-2008.
%F A145903 For n >= 2, T(n,k) = binomial(n,k)^2 - n/(n-1)*binomial(n-1,k-1)*binomial(n-1,k).
%e A145903 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.
%e A145903 Triangle starts
%e A145903 n\k|..0....1....2....3....4....5....6
%e A145903 =====================================
%e A145903 0..|..1
%e A145903 1..|..1....1
%e A145903 2..|..1....2....1
%e A145903 3..|..1....6....6....1
%e A145903 4..|..1...12...24...12....1
%e A145903 5..|..1...20...70...70...20....1
%e A145903 6..|..1...30..165..280..165...30....1
%e A145903 ...
%Y A145903 A001263, A008459, A051924 (row sums), A080721.
%K A145903 easy,nonn,tabl
%O A145903 0,5
%A A145903 _Peter Bala_, Oct 28 2008