Evaluate the sum ${n \choose 1} + 3{n \choose 3} +5{n \choose 5} + 7{n \choose 7}...$ in closed form How do I evaluate the sum:$${n \choose 1} + 3{n \choose 3} +5{n \choose 5} + 7{n \choose 7}  ...$$in closed form?
I don't really know how to start and approach this question. Any help is greatly appreciated.

Hint: We have $\binom{n}{2k-1}=\frac{n}{2k-1}\binom{n-1}{2k-2}$.
Note that $\binom{a}{b}=0$ if $b\gt a$.
