JEE Main 2022 · 25 Jul · Shift 2, Mathematics question 27

Let $a_n=\displaystyle\int_{-1}^n\left(1+\frac x2+\frac{x^2}3+\dots+\frac{x^{n-1}}n\right)dx$ 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 ______.