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Search: id:A072248
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| A072248 |
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Triangle T(n,k) (n>=2, 1<=k<=n-1) giving number of non-crossing trees with n nodes and height k. |
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+0
2
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| 1, 1, 2, 1, 7, 4, 1, 20, 26, 8, 1, 54, 126, 76, 16, 1, 143, 548, 504, 200, 32, 1, 376, 2259, 2900, 1656, 496, 64, 1, 986, 9034, 15506, 11528, 4896, 1184, 128, 1, 2583, 35469, 79354, 73172, 39552, 13536, 2752, 256, 1, 6764, 137644, 394642, 439272, 285992
(list; table; graph; listen)
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OFFSET
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0,3
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COMMENT
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For n>2 n-th row has n-2 terms.
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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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Column g.f. are T[k]-T[k-1] (k=1, 2, ...), where T[0]=z and T[k]=z/[1-T[k-1]^2/z]. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Dec 30 2004
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EXAMPLE
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1; 1,2; 1,7,4; 1,20,26,8; ...
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MAPLE
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T[0]:=z: for k from 1 to 10 do T[k]:=simplify(z/(1-T[k-1]^2/z)) od:for k from 1 to 10 do t[k]:=series(T[k]-T[k-1], z=0, 15) od: for n from 1 to 10 do seq(coeff(t[k], z^(n+1)), k=1..n) od; (Deutsch)
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CROSSREFS
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Cf. A001764, A072247. Row sums give A001764.
Sequence in context: A120903 A021050 A115629 this_sequence A092276 A011274 A122843
Adjacent sequences: A072245 A072246 A072247 this_sequence A072249 A072250 A072251
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KEYWORD
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nonn,tabl
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AUTHOR
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njas, Jul 06 2002
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EXTENSIONS
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More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Dec 30 2004
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