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A024718
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(1/2)*(1 + sum of C(2k,k)) for k = 0,1,2,...,n.
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12
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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; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Also: Number of UH-free Schroeder 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
Hankel transform is A010892. [From Paul Barry (pbarry(AT)wit.ie), Apr 28 2009]
Binomial transform of A005773. [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Dec 13 2009]
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LINKS
| Guo-Niu Han, Enumeration of Standard Puzzles
Sherry H. F. Yan, Schroeder Paths and Pattern Avoiding Partitions, arXiv:0805.2465 [math.CO] .
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FORMULA
| G.f.: 1/((1-x)*(2-C)) where C = g.f. for Catalan numbers A000108. N. J. A. Sloane (njas(AT)research.att.com), 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
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CROSSREFS
| Equals A079309(n) + 1. Partial sums of A088218. Bisection of A086905. Second column of triangle A102541.
Sequence in context: A020876 A149949 A149950 * A149951 A157135 A196836
Adjacent sequences: A024715 A024716 A024717 * A024719 A024720 A024721
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KEYWORD
| nonn
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AUTHOR
| Clark Kimberling (ck6(AT)evansville.edu)
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