|
| |
|
|
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
(list; table; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,3
|
|
|
COMMENTS
| For n>2 n-th row has n-2 terms.
|
|
|
REFERENCES
| E. Deutsch and M. Noy, Statistics on non-crossing trees, Discr. 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 (deutsch(AT)duke.poly.edu), Dec 30 2004
|
|
|
EXAMPLE
| 1; 1,2; 1,7,4; 1,20,26,8; ...
|
|
|
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 1 to 10 do seq(coeff(t[k], z^(n+1)), k=1..n) od; (Deutsch)
|
|
|
CROSSREFS
| Cf. A001764, A072247. Row sums give A001764.
Sequence in context: A021050 A115629 A144696 * A177011 A092276 A011274
Adjacent sequences: A072245 A072246 A072247 * A072249 A072250 A072251
|
|
|
KEYWORD
| nonn,tabl
|
|
|
AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Jul 06 2002
|
|
|
EXTENSIONS
| More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Dec 30 2004
|
| |
|
|
