In genera 0 and 1, some considerations from algebraic geometry (more precisely the ELSV formula, see [3]) yield explicit formula for [h.sup.0.sub.n]([lambda]) and [h.sup.1.sub.n]([lambda]), whence closed formula for series [H.sup.0]([lambda]) and [H.sup.1]([lambda]) (see Section 2.4).
In spherical or toric genus, one has closed formula stemming from the ELSV formula for one-partition Hurwitz numbers.