We prove the following conjecture of Zeilberger. Denoting by C n the Catalan number, define inductively A n by (-1) n-1A n=C n+∑ j=1n-1(-1)j(2n-1 2j-1)A jC n-j and a n=2A n/C n. Then a n (hence A n) is a positive integer. © 2012 Elsevier Inc.
Lassalle, M. (2012). Two integer sequences related to Catalan numbers. Journal of Combinatorial Theory. Series A, 119(4), 923–935. https://doi.org/10.1016/j.jcta.2012.01.002