\[\omega_{y}=\frac{{\left(\alpha+1\right)_{y}}{\left(\beta+\delta+1\right)_{y}}{%
\left(\gamma+1\right)_{y}}{\left(\gamma+\delta+2\right)_{y}}}{{\left(-\alpha+%
\gamma+\delta+1\right)_{y}}{\left(-\beta+\gamma+1\right)_{y}}{\left(\delta+1%
\right)_{y}}y!},\]