Let \( a_1 = b_1 = 1 \) and \( a_n = a_{n-1} + (n-1), b_n = b_{n-1} + a_{n-1}, \forall\, n \ge 2 \). If \( S = \ \displaystyle \sum_{n=1}^{10} \frac{b_n}{2^n} \) and \( T = \ \displaystyle \sum_{n=1}^{8} \frac{n}{2^{\,n-1}} \), then \( 2^7 (2S - T) \) is equal to ______.
