|
Search: id:A024718
|
|
|
| A024718 |
|
(1/2)*(1 + sum of C(2k,k)) for k = 0,1,2,...,n. |
|
+0
11
|
|
| 1, 2, 5, 15, 50, 176, 638, 2354, 8789, 33099, 125477, 478193, 1830271, 7030571, 27088871, 104647631, 405187826, 1571990936, 6109558586, 23782190486, 92705454896, 361834392116, 1413883873976, 5530599237776, 21654401079326
(list; graph; listen)
|
|
|
OFFSET
|
0,2
|
|
|
COMMENT
|
Also: Number of UH-free Schroder paths of semilength n with horizontal steps only at level less than two [see Yan]. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), May 24 2008
|
|
LINKS
|
Sherry H. F. Yan, Schroeder Paths and Pattern Avoiding Partitions, arXiv:0805.2465 [math.CO] .
|
|
FORMULA
|
G.f.: 1/((1-x)*(2-C)) where C = g.f. for Catalan numbers A000108. njas, Aug 30 2002
Total number of leaves in all rooted ordered trees with at most n edges. - Michael Somos Feb 14 2006
Given g.f. A(x), then x*A(x-x^2) is g.f. of A024494. - Michael Somos Feb 14 2006
G.f.: (1+1/sqrt(1-4x))/(2-2x). a(n)=binomial(2n-1,n). - Michael Somos Feb 14 2006
|
|
CROSSREFS
|
Equals A079309(n) + 1. Partial sums of A088218. Bisection of A086905. Second column of triangle A102541.
Adjacent sequences: A024715 A024716 A024717 this_sequence A024719 A024720 A024721
Sequence in context: A005751 A020876 A093129 this_sequence A007853 A060049 A107590
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Clark Kimberling (ck6(AT)evansville.edu)
|
|
|
Search completed in 0.002 seconds
|
