A curious polynomial interpolation of Carlitz-Riordan's -ballot numbers
arXiv:1311.7228
Abstract
We study a polynomial sequence defined as a solution of a -difference equation. This sequence, evaluated at -integers, interpolates Carlitz-Riordan's -ballot numbers. In the basis given by some kind of -binomial coefficients, the coefficients are again some -ballot numbers. We obtain in a combinatorial way another curious recurrence relation for these polynomials.
arXiv comment15 pages, some connections with J. Cigler's earlier work is mentioned