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 $\genfrac{<}{>}{0pt}{}{x}{k}$ inductively defined by $k/x \genfrac{<}{>}{0pt}{}{x}{k}= t\genfrac{<}{>}{0pt}{}{x-1}{k-1} +(1-t)\genfrac{<}{>}{0pt}{}{x-2}{k-2}$.