$\gamma_{n}=\dfrac{\Gamma\left(n+\alpha+1\right)\Gamma\left(n+\beta+1\right)%
\Gamma\left(n+\alpha+\beta+1\right)}{(2n+\alpha+\beta+1)(\Gamma\left(2n+\alpha%
+\beta+1\right))^{2}}2^{2n+\alpha+\beta+1}n!,$