  A {\em $1-$vertex triangulation} of an oriented compact surface $S$ of genus
$g$ is an embedded graph $T\subset S$ with a unique vertex such that all
connected components of $S\setminus T$ are triangles (adjacent to exactly 3
edges of $T$).
  This paper gives formulas enumerating such triangulations (up to equivalence)
on an oriented surface of given genus.
  {\em Une triangulation \`a un sommet} d'une surface orient\'ee compacte $S$
de genre $g$ est un graphe $T\subset S$ qui a un unique sommet et dont toutes
les faces (composantes connexes de $S\setminus T$) sont des triangles
(incidentes \`a trois ar\^etes de $T$).
  Cet article donne des formules permettant d'\'enum\'erer ces triangulations.
