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Unable to deduce an inequality related to an integral

I am given a coefficient to estimate as a assignment question. But I am unable to think how it must be true. Notations Let $l$ belongs to $\{1, 2,\ldots,a\}$ and $j$ belongs to $\{0,1,\ldots,n\}$. Assume that this equation holds $$ c_{l,j,n}=\frac{1}{2\pi i}\int_{|z+j+1|=\frac{1}{2}} R_n(t) (z+j+1)^{l-1}\mathrm{d}z. $$ where $$ R_n(t) = \frac{(n!)^{a-2r} ×(t-rn+1)_{rn} (t+n+2)_{rn}}{(t+1)_{n+1}}. $$ Also note […]