Let \( n \) be a positive integer. Let \( A=\displaystyle\sum_{k=0}^{n}(-1)^k \,{{}^n C_ k}\left[\left(\dfrac{1}{2}\right)^k+\left(\dfrac{3}{4}\right)^k+\left(\dfrac{7}{8}\right)^k+\left(\dfrac{15}{16}\right)^k+\left(\dfrac{31}{32}\right)^k\right] \). If \( 63A=1-\dfrac{1}{2^{30}} \), then \( n \) is equal to ____________.
