  We investigate the excitation dynamics of Rydberg atoms in ultracold atomic
samples by expanding the excitation probability and the correlation function
between excited atoms in powers of the isolated atom Rabi frequency $\Omega$.
In the Heisenberg picture, we give recurrence relations to calculate any order
of the expansions, which ere expected to be well-behaved for arbitrarily strong
interactions. For homogeneous large samples, we give the explicit form of the
expansions, up to $\Omega^4$, averaged over all possible random spatial
distributions of atoms, for the most important cases of excitation pulses and
interactions.
