Currently debian packages (and presumably redhat/suse/etc) ship with old style SysV init.d file.
Most distributions are now systemd based, and to be able to make use of it's additional features it would be useful have /lib/systemd/system/jenkins.service file.
This would allow features like systemd's restart functionality to work (useful when Jenkins occasionally crashes, etc). See discussion around this here: http://serverfault.com/questions/760552/how-to-use-automatic-restart-with-jenkins-on-systemd
Details of how provide both systemd unit file and SysV init file are detailed here:
This should be applicable to all distro, and systemd unit most likely the same across them all, as it's much more standardised than each distros SysV init infrastructure.