Hold up, if you can trigger notes, you can record the notes in the sequencer. The only exception is if you set your MIDI device up as an External Control bus, which is really meant for playing Reason devices by an external sequencer app.
That might explain why you can play, but not sequence. Instead of doing it like that, you can set it up in Keyboards and Control Surfaces. If it doesn't show up in the surface list, add it as an <Other> MIDI Control Keyboard.