%0 Journal Article %T Two integer sequences related to Catalan numbers %A Michel Lassalle %J Mathematics %D 2010 %I arXiv %X We prove the following conjecture of Zeilberger. Denoting by $C_n$ the Catalan number, define inductively $A_n$ by $(-1)^{n-1}A_n=C_n+\sum_{j=1}^{n-1} (-1)^{j} \binom{2n-1}{2j-1} A_j \,C_{n-j}$ and $a_n=2A_n/C_n$. Then $a_n$ (hence $A_n$) is a positive integer. %U http://arxiv.org/abs/1009.4225v4