Given a function (aka 'permutation') $f:A \rightarrow A$, where $A$ is a finite set such that $|A| = N$, we call it a self-inverse if $f(f(x)) = x$. The sequence of how many such functions exist for increasing cardinalities is given by OEIS A000085. As far as I can tell, there is only a recursive formula for this sequence, is there a general formula?