  We show that an infinite family of contractible 4-manifolds have the same
boundary as a special type of plumbing. Consequently their Ozsvath--Szabo
invariants can be calculated algorithmically. We run this algorithm for the
first few members of the family and list the resulting Heegaard--Floer
homologies. We also show that the rank of the Heegaard--Floer homology can get
arbitrary large values in this family by using its relation with the Casson
invariant. For comparison, we list the ranks of Floer homologies of all the
examples of Briekorn spheres that are known to bound contractible manifolds.
