Combinatorics Catastrophe How will you solve 
$$\sum_{i=1}^{n}{2i \choose i}\;?$$
I tried to use Coefficient Method but couldn't get it! Also I searched for Christmas Stocking Theorem but to no use ...

Maple gives a "closed form" involving a hypergeometric function:
$$ -1-{2\,n+2\choose n+1}\; {\mbox{$_2$F$_1$}(1,n+\frac32;\,n+2;\,4)}-\frac{i
\sqrt {3}}{3}
$$
