ARTCC Controller reported accidentally removing the flight plan of an active aircraft; and not following up sufficiently to find the aircraft. As a result the aircraft transited additional sectors without appropriate coordination.

Narrative

Aircraft X called from the ground at ZZZ1 for a squawk and said he'll be departing VFR to pick up his clearance in the air. A few minutes later he departed; called and was told to IDENT. He was identified; and cleared IFR to FL240; with clearance to deviate around weather. He was given direct when clear of the weather and proceeded on course. A few minutes later; I inadvertently removed the flight plan from the system; intending to remove an arrival for a nearby airport.When I did this; I realized that the Aircraft Y did not drop off and I removed Aircraft Y's flight plan. I immediately began a scan; looking for limited data blocks. I did not see the limited data block on Aircraft X.Aircraft X proceeded to fly through Sector AB and into Sector DE; without a data block and frequency changes.Sector FG did close in or near the timeframe of the incident; but I'm not sure if it was before or after the RS message.Although I am very cautious about the removal of flight plans; apparently I was not cautious enough. And even though; I did realize the RS was possibly done in error; I did not look into it enough to find the mistake.One; be more careful on RS messages. Two; if I do mess it up; look a the CID of the flight plan that was removed using the recall key on the keyboard.