  Consider factorizations into transpositions of an n-cycle in the symmetric
group S_n. To every such factorization we assign a monomial in variables w_{ij}
that retains the transpositions used, but forgets their order. Summing over all
possible factorizations of n-cycles we obtain a polynomial that happens to
admit a closed expression. From this expression we deduce a formula for the
number of 1-faced embeddings of a given graph.
