The harmonic numbers are given by $$H_n=\sum_{k=1}^n\frac{1}{k}.$$
Then we have
$$
\sum_{k=1}^{n}(-1)^k{n\choose k}{n+k\choose k}\sum_{i=1}^{k}\frac{1}{n+i}=(-1)^nH_n.
$$
I want to know if this identity exists in the literature. If not, how can we prove it? 

Hints, references or proof are all welcome.