  The vicious random walker problem on a one dimensional lattice is considered.
Many walkers take simultaneous steps on the lattice and the configurations in
which two of them arrive at the same site are prohibited. It is known that the
probability distribution of N walkers after M steps can be written in a
determinant form. Using an integration technique borrowed from the theory of
random matrices, we show that arbitrary k-th order correlation functions of the
walkers can be expressed as quaternion determinants whose elements are
compactly expressed in terms of symmetric Hahn polynomials.
