Swap Permutations in Scala

Given a non-negative integer N return the number of swap permutations of length N

A swap permutation is obtained from the identical permutation (1, 2, 3, ..., N) by applying the swap operation multiple times

A swap operation consists of picking two different items from the permutation and swapping them

You are allowed to swap an item at most once

Example:

Input: N = 3
Output: 4
Explanation: [
    [1, 2, 3],
    [1, 3, 2],
    [2, 1, 3],
    [3, 2, 1]
]
We start from [1, 2, 3], which is a swap permutation
because we  applied 0 swap operations, and we apply
one of the following swaps:
[1, 2, 3] => [1, 3, 2]
[1, 2, 3] => [2, 1, 3]
[1, 2, 3] => [3, 2, 1]
Notice that we can only apply one swap operation
because we are left with only 1 item that is not swapped.
For larger values of N we can have multiple chained operations.