2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/216266Extensions 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.9 pages, presented at the Gian-Carlo Rota Polish Seminar, http://ii.uwb.edu.pl/akk/sem/sem_rota.htmCombinatoricsDiscrete Mathematics05A40, 11B73, 81S99text