f(x) = x + \displaystyle\sum_{n=2}^{\infty} \frac{(3^n - 2^n) + n(3^{n-1} - 2^{n-1})+\frac{1}{2}n(n-1)(3^{n-2} - 2^{n-2})}{n!}x^n

\implies a_1 = 1, a_n = (3^n - 2^n) + n(3^{n-1} - 2^{n-1})+\frac{1}{2}n(n-1)(3^{n-2} - 2^{n-2}),\quad n \geq 2