280. What formula? Find the formula for the general term of the sequence $\left\{x_{n}\right\}$, defined recursively:

$$
x_{n}=(n-1)\left(x_{n-1}+x_{n-2}\right), \quad n \geqslant 4, \quad x_{2}=1, \quad x_{3}=2
$$
280. Assuming $x_{k}=k!y_{k}$, we get

$$
y_{k}-y_{k-1}=-\frac{1}{k}\left(y_{k-1}-y_{k-2}\right), \quad k \geqslant 4
$$

Using (1) for $k=4,5, \ldots, m$, we get

$$
y_{m}-y_{m-1}=\frac{(-1)^{m}}{m!}, \quad m \geqslant 4
$$

Summing the equalities (2) for $m=4,5, \ldots, n$, we will finally arrive at the answer

$$
x_{n}=n!\sum_{m=2}^{n} \frac{(-1)^{m}}{m!}
$$

Note that the last equality is also valid for $n=2,3$.

[A. Beiger, A. M. M., 76, 302 (March 1969).]