A curious polynomial interpolation of Carlitz-Riordan's q-ballot numbers
Abstract
We study a polynomial sequence Cn(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.
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