Name of the software
xpadneo (Advanced Linux Driver for Xbox One Wireless Gamepad)
Gamepad vibration (rumble) on xbox one bluetooth controllers doesn't seem to work with current gamepad driver, xboxdrv from repo doesn't recognize the controller. Xpadneo does and enables vibration. Also other great features like battery level indication and Trigger Force Feedback.
Is it open source?
Yes. GNU General Public License v3.0.
Theres no releases (at least yet), but it's updated fairly often (last commit 4 months ago).