What is the ruling on someone who has forgotten the number of expiations (kaffarat) due upon him and wishes to fast them? And is it permissible to combine the intention of fasting for expiation with the intention of fasting for Ramadan?

If you are unable to feed ten poor persons, or clothe them, or free a slave, then you must fast for three days with the intention of expiation. It is not permissible to combine this with the fasting of Ramadan. If you forget the number of expiations due upon you, then strive to estimate them, and then take the lesser, certain amount, because the default is the acquittal of one's responsibility. The more cautious approach is to make expiation for the number about which you are unsure, and it is sunnah for you to do so until your responsibility is certainly acquitted.