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