Inverse Mellin transform of products of gamma functions

Question

I want to calculate the inverse Mellin transform of products of 3 gamma functions. $$F\left ( s \right )=\frac{1}{2i\pi}\int \Gamma(s)\Gamma (2s+a)\Gamma( 2s+b)x^{-s}ds$$ Above contour integral has 3 poles. $$s_{1}=-n$$ $$s_{2}=-\left ( \frac{n+a}{2} \right )$$ $$s_{3}=-\left ( \frac{n+b}{2} \right )$$ Which pole is used in contour integral? $$F\left ( s \right )=\sum_{n=0}^{\infty }\frac{\left ( -1 \right )^{n}}{n!}\Gamma \left ( a-2n \right )\Gamma \left ( -2n+b \right )x^{n}+\sum_{n=0}^{\infty}\frac{\left ( -1 \right )^{n}}{n!}\Gamma \left ( -\frac{n}{2}-\frac{a}{2} \right)\Gamma \left ( -n-a+b\right )x^{\frac{n}{2}+\frac{a}{2}}+\sum_{n=0}^{\infty}\frac{(-1)^{n}}{n!}\Gamma \left (-\frac{n}{2}-\frac{b}{2} \right )\Gamma (-n-b+a)x^{\frac{n}{2}+\frac{b}{2}}$$ Is this correct??