Dobinski-type relations: Some properties and physical applications
  We introduce a generalization of the Dobinski relation through which we define a family of Bell-type numbers and polynomials. For all these sequences we find the weight function of the moment problem and give their generating functions. We provide a physical motivation of this extension in the context of the boson normal ordering problem and its relation to an extension of the Kerr Hamiltonian. 
P Blasiak (1), A Horzela (1), K A Penson (2), A I Solomon (2,3), ((1)   Polish Academy of Sciences, Krakow, Poland, (2) LPTL...