limsup and liminf of two classical sequences

Consider the sequences $(s_n)_{n\ge1}$ and $(t_n)_{n\ge1}$ defined by

$$s_n=\sum_{k=0}^n\frac1{(k!)^2}\quad\text{and}\quad t_n=\sum_{k=0}^n\binom nk\frac{(-1)^k}{n^k}.$$

Which of the following statements are true?