Fruits and Baskets Generalized

There are $n$ baskets of fruits in a line, with $n$ fruits also present. Each basket is designated to a certain fruit, and that fruit is placed inside it basket. How many ways can the fruits be rearrange such that no fruit is in its designated basket? Let $a_1$ denote the answer if $n = 1$ , $a_2$ denote the answer if $n = 2$ , and so on ( $a_n$ is the answer with $n$ fruits and baskets). If I know the values of $n-1, a_{n-1}$ , and $a_{n-2}$ , how many calculations must I make to find $a_n$ .

Details and Assumptions

• There is only one of each type of fruit.
• Each basket must contain exactly one fruit.