The father of a child which is or may be born out of lawful matrimony is liable to the same extent as the father of a child born of lawful matrimony, whether or not the child is born alive, for the reasonable expense of the mother’s pregnancy and confinement, and for the education, necessary support and maintenance, and medical and funeral expenses of the child. A child born out of lawful matrimony also includes a child born to a married woman by a man other than her lawful husband.