Partitions with Distinct Multiplicities of Parts: On An "Unsolved   Problem" Posed By Herbert Wilf
  Wilf's Sixth Unsolved Problem asks for any interesting properties of the set of partitions of integers for which the (nonzero) multiplicities of the parts are all different. We refer to these as \emph{Wilf partitions}. Using $f(n)$ to denote the number of Wilf partitions, we establish lead-order asymptotics for $\ln{f(n)}$. 
James Allen Fill and Svante Janson and Mark Daniel Ward
math.CO cs.DM