Series with a sum of odd numbers over factorial

Let $\{a_n\}_{n\ge1}$ be a sequence of real numbers such that

$$a_n=\frac{1+3+5+\cdots+(2n-1)}{n!},\quad n\ge1.$$

Then $\sum_{n\ge1}a_n$ converges to ____________ (round off to 2 decimal places)