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Search: id:A089627
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| A089627 |
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Triangle T(n,k), 0<=k<=n, read by rows, defined by T(n,k)=C(n,2*k)*C(2*k,k). |
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3
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| 1, 1, 0, 1, 2, 0, 1, 6, 0, 0, 1, 12, 6, 0, 0, 1, 20, 30, 0, 0, 0, 1, 30, 90, 20, 0, 0, 0, 1, 42, 210, 140, 0, 0, 0, 0, 1, 56, 420, 560, 70, 0, 0, 0, 0, 1, 72, 756, 1680, 630, 0, 0, 0, 0, 0, 1, 90, 1260, 4200, 3150, 252, 0, 0, 0, 0, 0
(list; table; graph; listen)
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OFFSET
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0,5
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COMMENT
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Row sums : A002426.
Contribution from Peter Bala (pbala(AT)toucansurf.com), Oct 28 2008: (Start)
The rows of this triangle are the gamma vectors of the n-dimensional type B associahedra (Postnikov et al., p.38 ). Cf. A055151 and A101280.
(End)
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LINKS
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A. Postnikov, V. Reiner, L. Williams, Faces of generalized permutohedra [From Peter Bala (pbala(AT)toucansurf.com), Oct 28 2008]
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FORMULA
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T(n, k) = n!/((n-2*k)!*k!*k!).
E.g.f.: exp(x)*BesselI(0, 2*x*sqrt(y)). - Vladeta Jovovic (vladeta(AT)eunet.rs), Apr 07 2005
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EXAMPLE
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Triangle begins:
1
1, 0
1, 2, 0
1, 6, 0, 0
1, 12, 6, 0, 0
1, 20, 30, 0, 0, 0
1, 30, 90, 20, 0, 0, 0
1, 42, 210, 140, 0, 0, 0, 0
1, 56, 420, 560, 70, 0, 0, 0, 0
1, 72, 756, 1680, 630, 0, 0, 0, 0, 0
1, 90, 1260, 4200, 3150, 252, 0, 0, 0, 0, 0
1, 110, 1980, 9240, 11550, 2772, 0, 0, 0, 0, 0, 0
1, 132, 2970, 18480, 34650, 16632, 924, 0, 0, 0, 0, 0, 0
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MAPLE
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for i from 0 to 12 do > seq( binomial(i, j)*binomial(i-j, j), j=0..i ); > od; - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 07 2006
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CROSSREFS
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Cf. A002426, A055151, A101280.
Sequence in context: A094456 A010028 A151860 this_sequence A055925 A161121 A021500
Adjacent sequences: A089624 A089625 A089626 this_sequence A089628 A089629 A089630
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KEYWORD
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easy,nonn,tabl
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AUTHOR
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DELEHAM Philippe (kolotoko(AT)wanadoo.fr), Dec 31 2003
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