Enumeration via ballot numbers

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Super Ballot Numbers

The Catalan numbers C n = (2n)!/n! (n + 1)! are are well-known integers that arise in many combinatorial problems. The numbers 6(2n)!/n! (n + 2)!, 60(2n)!/n! (n + 3)!, and more generally (2r + 1)!/r! · (2n)!/n! (n + r + 1)! are also integers for all n. We study the properties of these numbers and of some analogous numbers that generalize the ballot numbers, which we call super ballot numbers.

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ژورنال

عنوان ژورنال: Discrete Mathematics

سال: 2008

ISSN: 0012-365X

DOI: 10.1016/j.disc.2007.06.012