Is it possible to record a MIDI sequence?
I’m not sure exactly what you are asking. If you want a copy of the MIDI sequence, then you just copy the original MIDI file. It is the sequence. If you want to “see” or change the MIDI sequence, open it in a music sequencer program that lets you rearrange and modify the notes and assign them to instruments. If your midi sequence is coming from a MIDI input from an actual musical instrument or similar, rather than a MIDI file, again a music sequencer program should do the trick. You’ve already found out how to make a copy in in a WAV or MP3 format file. There are also format converters/transcoders that can do the same thing automatically at greater than playback speed. For example, on Linux, SoundKonverter supports this.