  Extensions of the $Stirling$ numbers of the second kind and $Dobinski$ -like
formulas are proposed in a series of exercises for graduates. Some of these new
formulas recently discovered by me are to be found in the source paper $ [1]$.
These extensions naturally encompass the well known $q$- extensions. The
indicatory references are to point at a part of the vast domain of the
foundations of computer science in arxiv affiliation.
