\[{{}_{3}F_{2}}\left({-n,a,1\atop-n,c};1\right)=\sum_{k=0}^{n}\frac{{\left(a%
\right)_{k}}}{{\left(c\right)_{k}}}=\frac{c-1}{c-a-1}\left(1-\frac{{\left(a%
\right)_{n+1}}}{{\left(c-1\right)_{n+1}}}\right),\]