Evaluate $\sum_{k=0}^n {{2n + 1}\choose {2k + 1}}$ Evaluate $$ \sum_{k=0}^n {{2n + 1}\choose {2k + 1}} $$
I'm really stuck on this one, no idea how to progress. My best guess is to somehow get it into the form of $ n\choose k $ and then take that summation and work with that. Or maybe binomial theorem, but I'm very experienced with that. If you could give a breakdown on how to tackle these problems that'd be great!

Hint:
$$2\sum_{k=0}^n\binom{2n+1}{2k+1}a^{2n-2k}b^{2k+1}=(a+b)^{2n+1}-(a-b)^{2n+1}=?$$
Set $a=b=1$
