Each parent of a child conceived or born out of wedlock is liable for the necessary support and education of the child and for the child’s funeral expenses. If a parent dies, an order of support or a judicially approved settlement made prior to that parent’s death shall be enforceable as a claim against the deceased parent’s estate in an amount to be determined by the probate court not greater than is provided in the order of settlement, having regard to the age of the child, the ability of the surviving parent to support and educate it, the amount of property left by the deceased parent, and the number, age and financial condition of those other persons legally entitled to support by the deceased parent during his or her lifetime.