Sum of the series \[ \sum_{k=0}^{2 m-1}(-1)^{k}\left(\begin{array}{...

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Sum of the series
\[
\sum_{k=0}^{2 m-1}(-1)^{k}\left(\begin{array}{l}
n \\
2 m-k
\end{array}\right)\left(\begin{array}{l}
n \\
k
\end{array}\right)
\]
(a) \( (-1)^{m}\left(\begin{array}{c}2 m \\ m\end{array}\right) \)
(b) \( (-1)^{m}\left(\begin{array}{l}n \\ m\end{array}\right)-\left(\begin{array}{c}n \\ 2 m\end{array}\right) \)
(c) 1
(d) \( { }^{2 m-1} C_{m-1} \)
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