Two integer sequences related to Catalan numbers

Michel Lassalle (1)

1 LIGM - Laboratoire d'Informatique Gaspard-Monge

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.

Domaines: Physique mathématique [math-ph]

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