no serial number

See this article:

Identify your AirPods - Apple Support

Note that depending on from exactly whom on “Amazon” you purchased your AirPods - there is a high probability that they are counterfeit.

And a single “known legitimate” serial number can be mass-counterfeited.

“Amazon’s” (proper) current price is only a few $$$ less than Apple’s “list price.”

If you paid a “lot” less … you probably received a “lot” less.

Not sure if in the recent models serial number is no more printed on the case. This also happened with iphones.. Old models had the serial on teh back, from a certain model onwards Apple no longer put it on.

Anyway you can check the serial from your iPad/iPhone in the bluetooth section once you paired your AirPods.

Go to bluetooth and press the "i" near the AirPods entry.. Then check the serial on Apple's site