For \( k \in N \), let \( \frac{1}{\alpha(\alpha+1)(\alpha+2) \ldots(\alpha+20)}=\sum_{ k =0}^{20} \frac{ A _{ k }}{\alpha+ k } \), where \( a >0 \). Then the value of 100 \( \left(\frac{A_{14}+A_{15}}{A_{13}}\right)^{2} \) is equal to
[Jee main \( 2021(20-07-2021 \)-shift-2)]