MC-finiteness of restricted set partition functions

A sequence $s(n)$ of integers is MC-finite if for every $m\in {\mathbb{N}}^{+}$ the sequence $s^m(n)=s(n)m$ is ultimately periodic. We discuss various ways of proving and disproving MC-finiteness. Our examples are mostly taken from set partition functions, but our methods can be applied to many more integer sequences.