The pdf below presents three creation / raising ops for an avatar of the refined Stirling partition polynomials of the second kind (OEIS A036040), also associated with Scherk, Touchard, and Steffensen, but most commonly linked to Bell and Faa di Bruno. These compositional polynomials and their kin and the combinatorial constructs they enumerate occur very frequently in investigations of quantum theory, combinatorial Hopf and other algebras, and nonlinear differential evolution equations.
Stirling Raisings: Creation Ops for the Faa di Bruno-Bell Polynomials (pdf)
Related Stuff:
“Integrable hierarchies, Hurwitz numbers and a branch point field in critical topologically massive gravity” by Mvondo-She
“Riccati Chain, Higher Order Painleve Type Equations, and Stabilizer Set of Virasoro Orbit” by Guha, see Defn. 4.4 on p.11. Eqn. 15 on p. 12 and eqn. 19 on p. 12 can be interpreted in terms of the action of 
Shadows of Simplicity 