fiNd a Closed Form for the Generating Function for the Sequence

Short Answer

find a closed form for the generating function for the sequence.
- $$\left( \begin{array} { l } 50 \\50\end{array} \right) , \left( \begin{array} { c } 50 \\49\end{array} \right) , \left( \begin{array} { c } 50 \\48\end{array} \right) , \ldots , \left( \begin{array} { c } 50 \\1\end{array} \right) , \left( \begin{array} { c } 50 \\0\end{array} \right) , 0,0,0 , \ldots$$