  We prove that graphs G, G' satisfy the same sentences of first-order logic
with counting of quantifier rank at most k if and only if they are
homomorphism-indistinguishable over the class of all graphs of tree depth at
most k. Here G, G' are homomorphism-indistinguishable over a class C of graphs
if for each graph F in C, the number of homomorphisms from F to G equals the
number of homomorphisms from F to G'.
