Sequences And Series

Let \(\{ {a_n}\} _{n = 0}^\infty\) be a sequence such that \({a_0} = {a_1} = 0\) and \({a_{n + 2}} = 2{a_{n + 1}} - {a_n} + 1\) for all n \(\ge\) 0. Then, \(\sum\limits_{n = 2}^\infty {{{{a_n}} \over {{7^n}}}}\) is equal to: