I have a homework assignment to find a recursive function for $k(n)$ where $k(n)$ is the number of ways to split the set $\{1,2,3,4....n\}$ while not having any subset contain more than two elements. for example $\{\{1,2\},\{3\},\{4\},\{5,6\}\}$ is an acceptable split of $k(6)$
I can't seem to figure out the recursive function for this.
Can someone please help me out?
Thanks.