Is the following identity known?

$$\sum\limits_{k=0}^n\frac{(-1)^k}{2k+1}\binom{n+k}{n-k}\binom{2k}{k}= \frac{1}{2n+1}$$

I have not found it in the following book:

- Henry Wadsworth Gould, Combinatorial identities: a standardized set of tables listing 500 binomial coefficient summations, Morgantown, West Virginia, 1972.