\sum\limits_{n \ge 2} {\frac{{s_n x^n }}{{n!}}} = \sum\limits_{n \ge 2} {\frac{{s_{n - 1} x^n }}{{n!}}} + \sum\limits_{n \ge 2} {\frac{{\left( {n - 1} \right)s_{n - 2} x^n }}{{n!}}}