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fiNd a Closed Form for the Generating Function for the Sequence

question 76

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find a closed form for the generating function for the sequence.
- (5050),(5049),(5048),,(501),(500),0,0,0,\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


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