The Stanely-F\'eray-\'Sniady formula for the generalized characters of   the Symmetric Group
  We show that the explicit formula of Stanley-F\'eray-\'Sniady for the characters of the symmetric group have a natural extension to the generalized characters. These are the spherical functions of the unbalanced Gel'fand pair $(S_n\times S_{n-1},\text{diag}S_{n-1})$. 
Fabio Scarabotti
math.RT