  We consider a new type of Hurwitz number, the number of ordered transitive
factorizations of an arbitrary permutation into d-cycles. In this paper, we
focus on the special case d = 3. The minimal number of transitive
factorizations of any permutation into 3-cycles has been worked out by David,
Goulden and Jackson. Also, such factorizations for transpositions, the case d =
2, have been considered by Crescimanno and Taylor. Goulden and Jackson have
proved the differential equation for the generating series of simple Hurwitz
numbers. Based on their results, we use W-operator to prove a differential
equation for the generating function of the new type Hurwitz number.
