I would be very grateful for any ideas to find a closed form for the sum:
$$ \sum^\infty_{k=0} \frac{z^k}{\Gamma(1+k) \Gamma(k+m+1)} {}_1F_2\left(1;1+k,m+k;z\right) $$
where $m\in\mathbb{N}$ and $z\in\mathbb{R}^+$.
I would be very grateful for any ideas to find a closed form for the sum: $$ \sum^\infty_{k=0} \frac{z^k}{\Gamma(1+k) \Gamma(k+m+1)} {}_1F_2\left(1;1+k,m+k;z\right) $$ where $m\in\mathbb{N}$ and $z\in\mathbb{R}^+$. 

