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Two integer sequences related to Catalan numbers

Abstract : We prove the following conjecture of Zeilberger. Denoting by C-n the Catalan number, define inductively A(n) by (-1)(n-1) A(n) = Cn + Sigma(n-1)(j=1) (-1)(j) ((2n-1)(2j-1))A(j)C(n-j) and a(n) = 2A(n)/C-n. Then a,, (hence A(n)) is a positive integer. (C) 2012 Elsevier Inc. All rights reserved.
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Contributor : Michel Lassalle Connect in order to contact the contributor
Submitted on : Wednesday, May 2, 2012 - 4:36:13 PM
Last modification on : Thursday, September 29, 2022 - 2:21:15 PM

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Michel Lassalle. Two integer sequences related to Catalan numbers. Journal of Combinatorial Theory, Series A, Elsevier, 2012, 119 (4), pp.923--935. ⟨10.1016/j.jcta.2012.01.002⟩. ⟨hal-00693432⟩



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