If the second term of the expansion ${\left[{\mathrm{a}}^{1/13}+\frac{\mathrm{a}}{\sqrt{{\mathrm{a}}^{-1}}}\right]}^{\mathrm{n}}$ is 14 a^5/2, then the value of $\frac{{ }^{\mathrm{n}}{\mathrm{C}}_3}{{ }^{\mathrm{n}}{\mathrm{C}}_2}$ is __________.

${\mathrm{T}}_2{=}^{\mathrm{n}}{\mathrm{C}}_1{\left({\mathrm{a}}^{1/13}\right)}^{\mathrm{n}-1}\cdot \mathrm{a}\sqrt{\mathrm{a}}=14{\mathrm{a}}^{5/2}$

or $\mathrm{n}\cdot {\mathrm{a}}^{\frac{\mathrm{n}-1}{13}}=14\mathrm{a}$

$\begin{array}{c}\mathrm{or} \mathrm{n}\cdot {\mathrm{a}}^{\frac{\mathrm{n}-14}{13}}=14\\ \mathrm{or} \frac{\mathrm{n}-14}{13}=0\\ \mathrm{or} \mathrm{n}=14\\ \Rightarrow \frac{{ }^{14}{\mathrm{C}}_3}{{ }^{14}{\mathrm{C}}_2}=\frac{14!}{3!\cdot 11!}\frac{2!\cdot 12!}{14!}=\frac{12}{3}=4\end{array}$