Does expiation become obligatory for one who swore not to commit a specific sin, then committed it, having forgotten his oath?

No expiation is required for you if you violate an oath due to forgetfulness. However, the oath remains binding. If you commit the disobedience intentionally and while remembering, then an expiation for the oath is incumbent upon you. This is in accordance with the Almighty's saying: (Our Lord, do not take us to task if we forget or make a mistake), and the Prophet's (peace be upon him) saying: (My Ummah has been forgiven for mistakes, forgetfulness, and what they are coerced into).