\[\sum_{j=0}^{n-1}\frac{x^{j}}{(j!)^{3}}=\frac{1}{2i}\int_{\mathscr{C}}\frac{x^{%
t}}{(\Gamma\left(t+1\right))^{3}}\cot\left(\pi t\right)\,\mathrm{d}t,\]