When you buy a product, the serial number should be sent to your email address or you can retrieve it from the My Account on the developer's website (in case that exists). Also, some emails are trapped because of the SPAM filters, therefore access that folder because the serial number might be in one of those emails.
If you find it, mark it as Safe so the service will restore it to the Inbox instead of SPAM for future emails.
If it's still not there, contact the developers of the application and request a status updated regarding the issue process of your serial numbers.