What is the ruling on a husband having sexual intercourse with his wife after saying, "It is unlawful for me, I do not know," while in a state of heedlessness, despite knowing the information, and before performing the expiation for the oath?

As long as you did not intend divorce or ẓihār (a pre-Islamic form of divorce by likening one's wife to one's mother) with this oath, then its ruling is that of an oath by Allah. Therefore, there is no sin upon you in having intercourse with your wife, and nothing is required of you in this regard. However, you must repent to Allah from lying and from the perjured oath (al-yamīn al-ghamūs). Some scholars obligate an expiation for the perjured oath, which is feeding ten poor people, or clothing them, or freeing a slave. If you cannot find these, then fasting for three days.