The question of whether a father should pay rent for an unmarried mother of his child is often a matter of legal and moral consideration. In many cases, if the father is legally obligated to provide child support, this may include contributing to the child's housing expenses, which could potentially include rent. However, each situation is unique, and various factors may influence the decision, such as

1. The financial resources and responsibilities of both parents.
2. The custody arrangements for the child
3. Any legal agreements or court orders in place.

Ultimately, it's advisable for both parties to seek legal advice to determine their rights and responsibilities in such situations.