[math-fun] Closed form for series?

Is there a closed form for the series sum(n^p z^n / n!, n=1..infinity) , where p is complex, or at least p > 0, or even just for p = 1/2 ?

-- Gene

Gene, this would require an analytic interpolation of the Bell polynomials analogous to Hurwitz zeta interpolating the Bernoulli polynomials. --Bill