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 A072248 Triangle T(n,k) (n >= 2, 1 <= k <= n-1) giving number of non-crossing trees with n nodes and height k. 1
 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, 123904, 35712, 6272, 512 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 2,3 COMMENTS For n >= 2, the n-th row has n-1 terms. LINKS E. Deutsch and M. Noy, Statistics on non-crossing trees, Discrete Math., 254 (2002), 75-87. FORMULA 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, Dec 30 2004 EXAMPLE Triangle T(n,k) begins: 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; MAPLE 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 2 to 11 do seq(coeff(t[k], z^n), k=1..n-1) od; # Emeric Deutsch, Dec 30 2004 CROSSREFS Cf. A001764, A072247. Row sums give A001764. Sequence in context: A115629 A296461 A144696 * A317360 A177011 A092276 Adjacent sequences:  A072245 A072246 A072247 * A072249 A072250 A072251 KEYWORD nonn,tabl AUTHOR N. J. A. Sloane, Jul 06 2002 EXTENSIONS More terms from Emeric Deutsch, Dec 30 2004 STATUS approved

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Last modified January 16 21:37 EST 2019. Contains 319206 sequences. (Running on oeis4.)