Frédéric Chapoton, Jiang Zeng
Published 2013-11-28, updated 2013-12-16Version 2
We study a polynomial sequence $C_n(x|q)$ defined as a solution of a $q$-difference equation. This sequence, evaluated at $q$-integers, interpolates Carlitz-Riordan's $q$-ballot numbers. In the basis given by some kind of $q$-binomial coefficients, the coefficients are again some $q$-ballot numbers. We obtain in a combinatorial way another curious recurrence relation for these polynomials.
Comments: 15 pages, some connections with J. Cigler's earlier work is mentioned
Multiple analogues of binomial coefficients and related families of special numbers
Factors of sums involving $q$-binomial coefficients and powers of $q$-integers
On some series involving the binomial coefficients $\binom{3n}{n}$
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