A new generalization of binomial coefficients

Abstract

Let $t$ be a fixed parameter and $x$ some indeterminate. We give some properties of the generalized binomial coefficients $\genfrac{}{}{0ex}{}{x}{k}$ inductively defined by $k/x\genfrac{}{}{0ex}{}{x}{k}=t\genfrac{}{}{0ex}{}{x-1}{k-1}+(1-t)\genfrac{}{}{0ex}{}{x-2}{k-2}$.

13 pages, LaTeX, to appear in Ramanujan Journal