Sequences And Series

For k \(\in\) N, let \({1 \over {\alpha (\alpha + 1)(\alpha + 2).........(\alpha + 20)}} = \sum\limits_{K = 0}^{20} {{{{A_k}} \over {\alpha + k}}}\), where \(\alpha > 0\). Then the value of \(100{\left( {{{{A_{14}} + {A_{15}}} \over {{A_{13}}}}} \right)^2}\) is equal to _____________.