\[{{}_{3}F_{2}}\left({-n,b,c\atop 1-b-n,1-c-n};1\right)=\begin{cases}0,&n=2k+1,%
\\
\dfrac{(2k)!\Gamma\left(b+k\right)\Gamma\left(c+k\right)\Gamma\left(b+c+2k%
\right)}{k!\Gamma\left(b+2k\right)\Gamma\left(c+2k\right)\Gamma\left(b+c+k%
\right)},&n=2k,\\
\end{cases}\]