Air Carrier Captain reported mechanics finding impact damage on engine cowling during post-flight inspection. Reporter suggested damage could have resulted from hitting a drone on takeoff.

Narrative

On Day 0 at around XA:00 local time; I operated flight Aircraft X from OKBK to ZZZZ. Conditions were unrestricted VFR from takeoff to landing; but it was all in the middle of the night. The aircraft had a light load (only 51 passengers; I believe; and not much cargo). This flight was the first of two legs that night; and we had 4 working pilots onboard including myself (total compliment of 2 Captains and 2 First Officers (FO)). The entire flight went without any issues from the moment we pushed back to the moment we shut down engines and opened the door. No one saw anything out of the ordinary and no one heard anything; this includes the Flight Attendants (FA); mechanics; and operations representatives in the cabin. There were no indications from the flight deck that anything had happened during the entire flight. Takeoff was normal and landing was normal. After landing at ZZZZ; the mechanics performed their post-flight inspection and found pretty serious impact damage on the right engine cowling. From the damage; it was clear that we hit something; but no one is sure when it could have happened. Based on the statements made from the rest of the crew and operations representatives; none of us believe that this impact occurred on the ground. It had to have happened somewhere in-flight; but the damage did not seemingly show signs of a bird strike. The theory that made the most sense to all of us was that it was possible we may have hit a drone on takeoff. I had been in OKBK for almost 6 days prior to this flight; and the week was leading up to some big national holiday in the country. During my time outside I did see a lot of drones being flown; so it's possible we may have collided with one; but none of us know for sure. We do strongly believe that it could not have happened on the ground. The operations representatives oversaw loading of the aircraft until the cargo doors were closed on that side of the aircraft; so we do not believe it could have been ground equipment. In OKBK; we taxied from Stand XXX via multiple taxiways; W4 W1 to Runway 33L. All taxiways were plenty wide and there were no possible obstacles that reach that high to cause such damage. At ZZZZ we landed on Runway XXR and taxied to the main ramp and we were watched the entire time. After our discovery; we notified ZZZZ tower to check for possible FOD and they found nothing.