Definite Integration

Let \({a_n} = \int\limits_{ - 1}^n {\left( {1 + {x \over 2} + {{{x^2}} \over 3} + \,\,.....\,\, + \,\,{{{x^{n - 1}}} \over n}} \right)dx}\) for every n \(\in\) N. Then the sum of all the elements of the set {n \(\in\) N : a_n \(\in\) (2, 30)} is ____________.