Technician reported supervising two apprentice mechanics on a nose landing tire change and signed off logbook for the completed work. Upon takeoff the nose landing gear failed to retract due to the nose landing gear downlock pin wasn't removed.

Narrative

On Day 0 during a periodic SVC (service) check. I got involve with both nose tire change. And got two apprentice mechanic's sent to help for the replace procedure. They replaced the tire under my supervision. And at the last minute I got involve with the procedure of all the s/n (serial number) and p/n (promissory note) to sign the log book. I went back to the office to complete the check of the logbook. To bring the logbook back to the airplane to avoid a delay. Thinking that the apprentice will clear and clean everything behind like taking the jack; the tires and removing the nose gear pin that they installed. But unfortunately they never removed the nose gear pin. And I as the mechanic in charge sign the tire change paper work. The airplane took off and the nose gear never came up. Coming back to base for to removing the pin and securing pin and gear. Having a delay but getting the airplane back to service safely. That day on around XA:30 I fill a report and applied the submit part. And then went home. For my surprise early next day I have a phone call from my supervisor; telling me that the report didn't went true and I have only 48 hours to fill the report. I apologize of filling the report application on Day 6. Five days after due to a mayor surgery that was happening Day 1. And not able to come to work or perform the report.Suggestions: From now on I will double check every detail on the job I have to sign.