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Search: id:A100400
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| A100400 |
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Triangle read by rows: T(n,k) is the number of nonroot nodes of outdegree k (0<=k<=n-1) in all non-crossing trees with n edges. |
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1
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| 1, 4, 2, 21, 12, 3, 120, 72, 24, 4, 715, 440, 165, 40, 5, 4368, 2730, 1092, 312, 60, 6, 27132, 17136, 7140, 2240, 525, 84, 7, 170544, 108528, 46512, 15504, 4080, 816, 112, 8, 1081575, 692208, 302841, 105336, 29925, 6840, 1197, 144, 9, 6906900, 4440150, 1973400, 708400, 212520, 53130, 10780, 1680, 180, 10
(list; table; graph; listen)
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OFFSET
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1,2
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COMMENT
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Row n contains n terms. Row sums yield A004319. Column 0 yields A045721.
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REFERENCES
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E. Deutsch and M. Noy, Statistics on non-crossing trees, Discr. Math., 254 (2002), 75-87.
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FORMULA
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T(n, k)=(k+1)binomial(3n-k-2, 2n-1) (0<=k<=n-1).
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EXAMPLE
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T(2,1)=2 because in the non-crossing trees /_, _\ and /\ we have 2 nonroot nodes of outdegree 1.
Triangle begins:
1;
4,2;
21,12,3;
120,72,24,4;
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MAPLE
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for n from 1 to 10 do seq((k+1)*binomial(3*n-k-2, 2*n-1), k=0..n-1) od; # yields sequence in triangular form
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CROSSREFS
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Cf. A001764, A004319, A045721.
Sequence in context: A081797 A016517 A157407 this_sequence A030211 A134461 A058167
Adjacent sequences: A100397 A100398 A100399 this_sequence A100401 A100402 A100403
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KEYWORD
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nonn,tabl
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AUTHOR
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Emeric Deutsch (deutsch(AT)duke.poly.edu), Dec 30 2004
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