Counting One-Vertex Maps
  The number of distinct maps (pre-maps) with a single vertex and valence $d$ is computed for any value of $d$. The types of maps (pre-maps) that we consider depend on whether the underlaying graph (pre-graph) is signed or unsigned and directed or undirected. 
Alen Orbanic, Marko Petkovsek, Tomaz Pisanski, Primoz Potocnik