For \( k\in\mathbb{N} \), let \( \dfrac{1}{\alpha(\alpha+1)(\alpha+2)\ldots(\alpha+20)}=\displaystyle\sum_{k=0}^{20}\dfrac{A_{k}}{\alpha+k} \), where \( \alpha>0 \). Then the value of \( 100\left(\dfrac{A_{14}+A_{15}}{A_{13}}\right)^{2} \) is equal to ________.
