The $n$-th harmonic number is defined as
$$
H_n=\sum_{k=1}^{n}\frac{1}{k},
$$
and the generalized harmonic numbers are defined by
$$
H_{n}^{(r)}=\sum_{k=1}^{n}\frac{1}{k^r}.
$$
Recently, I have found the following combinatorial identity involving the second-order harmonic numbers (I have computational evidence).

**Question:**
\begin{align}
\sum_{s=0}^{m}{2s\choose s}{s\choose m-s}\frac{(-1)^s H_{s}^{(2)}}{s+1}=\frac{2(-1)^m}{m+1}\sum_{s=0}^m H_{s}^{(2)}. 
\end{align}
Is this a known combinatorial identity? Any proof or reference?
However, if I replace $H_s^{(2)}$ by other generalized harmonic numbers in the above identity, I can not find some similar identities.

**NOte:**
This combinatorial identity was motivated by the following identity
\begin{align}
\sum_{s=0}^{m}{2s\choose s}{s\choose m-s}\frac{(-1)^s}{s+1}=(-1)^m.
\end{align}
One can refer to [How to prove $\sum_{s=0}^{m}{2s\choose s}{s\choose m-s}\frac{(-1)^s}{s+1}=(-1)^m$?](http://math.stackexchange.com/questions/1559612/how-to-prove-sum-s-0m2s-choose-ss-choose-m-s-frac-1ss1-1m)

I appreciate any hints, pointers etc.!