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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

Table of n, a(n) for n=2..56.

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 October 18 12:52 EDT 2018. Contains 316321 sequences. (Running on oeis4.)