  Summation of a large class of the functional series, which terms contain
factorials, is considered. We first investigated finite partial sums for
integer arguments. These sums have the same values in real and all p-adic
cases. The corresponding infinite functional series are divergent in the real
case, but they are convergent and have p-adic invariant sums in p-adic cases.
We found polynomials which generate all significant ingredients of these series
and make connection between their real and p-adic properties. In particular, we
found connection of one of our integer sequences with the Bell numbers.
