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I've looked through the user guide and the Central gui, and I can't figure out how to get an AP inventory report to include the serial numbers of my APs.
Unfortunately, today there is no UI option to do so.
There have been requests from the field and they are being looked at.
You could leverage the Central API to build a query for a device inventory. Please see the Central Help for further information and documentation on the API: http://help.central.arubanetworks.com/2.4.6/documentation/online_help/content/api_documentation/public%20cloud/api_bootstrapping.htm
This was explained in great detail by an Aruba SE who did this for one of our large customers:
https://community.arubanetworks.com/t5/Network-Management/Aruba-Central-API-Gateway-and-how-to-create-a-CSV-file-using/td-p/311618
Let us know if it helps