  This paper is devoted to the computation of the number of ordered
factorizations of a long cycle in the symmetric group where the number of
factors is arbitrary and the cycle structure of the factors is given. Jackson
(1988) derived the first closed form expression for the generating series of
these numbers using the theory of the irreducible characters of the symmetric
group. Thanks to a direct bijection we compute a similar formula and provide
the first purely combinatorial evaluation of these generating series.
