Please find a specific summation as follows.
$\sum^{i-1}_{k=1} k \frac{2a(n-(k-1))!}{(k-1-r_1)!(k-1-r_2)!(k-1-r_3)!}$
Calculate the sum the specific equation, which has k, denominator with three factorials and nominator with one factorial. Please help to find a solution. Thank you.