Michel Lassalle
Published 2010-09-21, updated 2012-01-10Version 4
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.
Comments: 15 pages, LaTeX, to appear in Journal of Combinatorial Theory, Series A
Journal: Journal of Combinatorial Theory, Series A 119 (2012), 923-935
Two proofs of the $q,t$-symmetry of the generalized $q,t$-Catalan number $C_{(k_1,k_2,k_3)}(q,t)$
Proof of a conjecture of Hadwiger
$q,t$-Catalan numbers and generators for the radical ideal defining the diagonal locus of $(\C^2)^n$
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