I need to evaluate the following complex integral (which is essentially an inverse Mellin transform): $$\int_{-c-i\infty}^{-c+i\infty} \Gamma^2 (-s) \Gamma (s+1) \Gamma (a-s) \mbox{}_1F_1(s;1;-y) x^s{\rm d}s,$$ where $a, x, y\geq 0$ and $-1<\Re[c]<0$.
I guess it is impossible to find the closed-form expression (even in terms of very complex functions, like hypergeometric ones), but at least I want to “estimate” it in terms of its approximation via finite sum of residues (for example). But for now I did not manage to be successful.