  For finite sums of non-negative powers of arithmetic progressions the
generating functions (ordinary and exponential ones) for given powers are
computed. This leads to a two parameter generalization of Stirling and Eulerian
numbers. A direct generalization of Bernoulli numbers and their polynomials
follows. On the way to find the Faulhaber formula for these sums of powers in
terms of generalized Bernoulli polynomials one is led to a one parameter
generalization of Bernoulli numbers and their polynomials. Generalized Lah
numbers are also considered.
