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.(read more)