  Umbral extensions of the stirling numbers of the second kind are considered
and the resulting dobinski-like various formulas including new ones are
presented. These extensions naturally encompass the two well known
q-extensions. The further consecutive umbral extensions q-stirling numbers are
therefore realized here in a two-fold way. The fact that the umbral q-extended
dobinski formula may also be interpreted as the average of powers of random
variable with the q-poisson distribution singles out the q-extensions which
appear to be a kind of singular point in the domain of umbral extensions as
expressed by corresponding two observations. Other relevant possibilities are
tackled with the paper`s closing down questions and suggestions with respect to
other already existing extensions while a brief limited survey of these other
type extensions is being delivered. There the newton interpolation formula and
divided differences appear helpful and inevitable along with umbra symbolic
language in describing properties of general exponential polynomials of
touchard and their possible generalizations. Exponential structures or
algebraically equivalent prefabs with their exponential formula appear to be
also naturally relevant.
