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Search: id:A060941
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| A060941 |
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Duchon's numbers: the number of paths of length 5*n from the origin to the line y=2*x/3 with unit East and North steps that stay below the line or touch it. |
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+0
2
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| 1, 2, 23, 377, 7229, 151491, 3361598, 77635093, 1846620581, 44930294909, 1113015378438, 27976770344941, 711771461238122, 18293652115906958, 474274581883631615, 12388371266483017545, 325714829431573496525
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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A generalization of the ballot numbers
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REFERENCES
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Cyril Banderier and Philippe Flajolet, Basic Analytic Combinatorics of Lattice Paths, Theoret. Comput. Sci. 281 (2002), 37-80.
Philippe Duchon, On the enumeration and generation of generalized Dyck words, Discrete Mathematics 225, 2000, 121-135
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LINKS
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C. Banderier, Home page
Cyril Banderier, Philippe Flajolet, Basic Analytic Combinatorics of Lattice Paths, Theoret. Comput. Sci. 281 (2002), 37-80.
M. Bousqet-Melou and A. Jehanne, Polynomial equations with one catalytic variable, algebraic series and map enumeration
P. Duchon, Home page
P. Duchon, Home Page [URL corrected by Gerald McGarvey, Oct 01 2009]
Philippe Duchon, On the enumeration and generation of generalized Dyck words, Discrete Mathematics 225, 2000, 121-135.
P. Flajolet, Home page
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FORMULA
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add(1/(5 * n+i+1) * binomial(5 * n+1, n-i) * binomial(5 * n+2 * i, i), i = 0..n); add((-1)^n1/(5 * n1+1) * binomial((5 * n1+1)/2, n1) * 1/(1+5 * (2 * n-n1)) * binomial((1+5 * (2 * n-n1))/2, 2 * n-n1), n1 = 0..2 * n);
G.f. satisfies A(z) = 1+2z^5A^5-z^5A^6+z^5A^7+z^10A^10.
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CROSSREFS
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Sequence in context: A088641 A013526 A091693 this_sequence A119774 A074649 A134355
Adjacent sequences: A060938 A060939 A060940 this_sequence A060942 A060943 A060944
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KEYWORD
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nice,nonn
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AUTHOR
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Philippe Flajolet (Philippe.Flajolet(AT)inria.fr), May 12 2001
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EXTENSIONS
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Updated Duchon URL - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 01 2009
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