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A080721
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Triangle of binomial(n,k)*(binomial(n+k,k)-binomial(n+k-2,k-1)).
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4
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1, 1, 1, 1, 4, 4, 1, 9, 21, 14, 1, 16, 66, 100, 50, 1, 25, 160, 410, 455, 182, 1, 36, 330, 1260, 2310, 2016, 672, 1, 49, 609, 3220, 8610, 12222, 8778, 2508, 1, 64, 1036, 7224, 26250, 53592, 61908, 37752, 9438, 1, 81, 1656, 14700, 69300, 189882, 312312, 303732, 160875, 35750, 1
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OFFSET
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0,5
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COMMENTS
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For n>1 and 0 <= k <= n, a(n,k) is the number of compatible k-sets of cluster variables in Fomin and Zelevinsky's 'cluster algebra' of finite type D_n.
Triangle of f-vectors of the simplicial complexes dual to the generalized associahedra of type D_n (n >= 2). See A145903 for the corresponding triangle of h-vectors. For the triangles of f-vectors of type A and type B associahedra see A033282 and A063007 respectively. [Peter Bala, Oct 28 2008]
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LINKS
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EXAMPLE
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Contribution from Peter Bala, Oct 28 2008: (Start)
Triangle begins
n\k|..0....1....2....3....4....5
================================
0..|..1
1..|..1....1
2..|..1....4....4
3..|..1....9...21...14
4..|..1...16...66..100...50
5..|..1...25..160..410..455..182
...
(End)
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MAPLE
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binomial(n, k)*(binomial(n+k, k)-binomial(n+k-2, k-1))
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MATHEMATICA
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Flatten[Table[Binomial[n, k](Binomial[n+k, k]-Binomial[Abs[n+k-2], k-1]), {n, 0, 10}, {k, 0, n}]] (* Harvey P. Dale, Feb 20 2013 *)
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PROG
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(PARI)
T(n, k)=binomial(n, k)*(binomial(n+k, k)-binomial(n+k-2, k-1))
for (n=0, 10, for (k=0, n, print1(T(n, k), ", ")));
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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