The comes from partitioning the n elements into 1 set of size 3 and n - 3 sets of size 1.

Then you have to add the number of ways of partitioning the n elements into 2 sets of size 2 and n - 4 sets of size 1. This is equal to (the number of ways of choosing 4 elements from the n elements) times (number of ways of choosing 2 elements from 4)/2:

.

You divide by 2 because otherwise you've double counted .... Think about it.