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Search: id:A092276
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| A092276 |
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Triangle read by rows: T(n,k) is the number of noncrossing trees with root degree equal to k. |
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4
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| 1, 2, 1, 7, 4, 1, 30, 18, 6, 1, 143, 88, 33, 8, 1, 728, 455, 182, 52, 10, 1, 3876, 2448, 1020, 320, 75, 12, 1, 21318, 13566, 5814, 1938, 510, 102, 14, 1, 120175, 76912, 33649, 11704, 3325, 760, 133, 16, 1, 690690, 444015, 197340, 70840, 21252, 5313, 1078, 168
(list; table; graph; listen)
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OFFSET
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1,2
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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.
M. Noy, Enumeration of noncrossing trees on a circle, Discrete Math., 180, 301-313, 1998.
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FORMULA
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T(n, k)=2k*binomial(3n-k, n-k)/(3n-k). G.f. = 1/(1-tzg^2), where g := 2*sin(arcsin(3*sqrt(3*z)/2)/3)/sqrt(3*z) is the g.f. of the sequence A001764.
T(n, k) = Sum_{j, j>=1} j*T(n-1, k-2+j) . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Sep 14 2005
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EXAMPLE
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1; 2,1; 7,4,1; 30,18,6,1; 143,88,33,8,1;
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MAPLE
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T := proc(n, k) if k=n then 1 else 2*k*binomial(3*n-k, n-k)/(3*n-k) fi end: seq(seq(T(n, k), k=1..n), n=1..11);
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CROSSREFS
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Row sums give sequence A001764.
First column gives sequence A006013.
Sequence in context: A021050 A115629 A072248 this_sequence A011274 A122843 A107865
Adjacent sequences: A092273 A092274 A092275 this_sequence A092277 A092278 A092279
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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), Feb 24 2004
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