Binomial Coefficient of Half

Theorem
Let $k \in \Z$.


 * $\dbinom {\frac 1 2} k = \dfrac {\left({-1}\right)^{k - 1} } {4^k \left({2 k - 1}\right)} \dbinom {2 k} k$

where $\dbinom {\frac 1 2} k$ denotes a binomial coefficient.