Sequences And Series

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 \(S = \sum\limits_{n = 1}^{10} {{{{b_n}} \over {{2^n}}}}\) and \(T = \sum\limits_{n = 1}^8 {{n \over {{2^{n - 1}}}}}\), then \({2^7}(2S - T)\) is equal to ____________.