Mathematics – Combinatorics
Scientific paper
2010-09-21
Mathematics
Combinatorics
15 pages, LaTeX, to appear in Journal of Combinatorial Theory, Series A
Scientific paper
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.
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