Refinement types have recently been applied to program verification, where program verification problems are reduced to type checking or inference problems. For fully automated verification of programs with recursive data structures, however, previous refinement type systems have not been satisfactory: they were not expressive enough to state complex properties of data, such as the length and monotonicity of a list, or required explicit declarations of precise types by users. To address the problem above, we introduce parameterized recursive refinement types (PRRT), which are recursive datatypes parameterized by integer parameters and refinement predicates; those parameters can be used to express various properties of data structures such as the length/sortedness of a list and the depth/size of a tree. We propose an automated type inference algorithm for PRRT, by a reduction to the satisfiability problem for CHCs (Constrained Horn Clauses). We have implemented a prototype verifier and evaluated the effectiveness of the proposed method through experiments.