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Search: id:A094040
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| A094040 |
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Triangle read by rows: T(n,k) is the number of noncrossing forests with n vertices and k edges. |
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1
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| 1, 1, 1, 1, 3, 3, 1, 6, 14, 12, 1, 10, 40, 75, 55, 1, 15, 90, 275, 429, 273, 1, 21, 175, 770, 1911, 2548, 1428, 1, 28, 308, 1820, 6370, 13328, 15504, 7752, 1, 36, 504, 3822, 17640, 51408, 93024, 95931, 43263, 1, 45, 780, 7350, 42840, 162792, 406980, 648945
(list; table; graph; listen)
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OFFSET
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1,5
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COMMENT
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T(n,n-1) yields A001764; T(n,n-2) yields A026004.
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REFERENCES
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P. Flajolet and M. Noy, Analytic combinatorics of noncrossing configurations, Discrete Math. 204 (1999), 203-229.
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FORMULA
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T(n, k)=binomial(n, k+1)*binomial(n+2k-1, k)/(n+k) (0<=k<=n-1).
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EXAMPLE
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1; 1,1; 1,3,3; 1,6,14,12; 1,10,40,75,55; 1,15,90,275,429,273;
T(3,1)=3 because the noncrossing forests on 3 vertices A,B,C and having one edge are (A, BC), (B, CA) and (C, AB).
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MAPLE
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T:=proc(n, k) if k<=n-1 then binomial(n, k+1)*binomial(n+2*k-1, k)/(n+k) else 0 fi end: seq(seq(T(n, k), k=0..n-1), n=1..11);
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CROSSREFS
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Cf. A001764, A026004.
Sequence in context: A082009 A110640 A143389 this_sequence A039798 A001498 A138464
Adjacent sequences: A094037 A094038 A094039 this_sequence A094041 A094042 A094043
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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), May 31 2004
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