For $2 \leq i \leq n$, 
\begin{flalign*}
A_i =\frac{\sum_{j=1}^{i-1} {{i-j} \choose {j}} 
\left[ (D_{i-j}\sum_{k=1}^{j} L_k)
{{n+m-i} \choose {m-j}}+(L_{i-j}\sum_{k=1}^{j} D_k) 
{{n+m-i}\choose {n-j}}
\right]}
{{{n+m} \choose n }} &&
\end{flalign*}