This Christmas sequence may have originally been written by St Bernard of Clairvaux, although some think it was written earlier. The theory arises in part because of the friendship of Sts Bernard and Norbert, as this sequence was originally part of the Praemonstratensian (Norbertine) liturgy.
This is the Dominican version, which is sung in the Dominican rite 3 times a year: the third Mass on Christmas, Epiphany, and the Presentation of the Lord.
I understand that the sequence “follows” the tune of the Alleluia–hence the name “sequence.” I would very much like to be pointed to scholarship about this, and in particular to learn how/ whether the sequences in current use “follow” the melodies of their past or present Alleluias.
My understanding is that the sequence as a genre grew out of "troping" the jubilus (the melismatic conclusion of the alleluia chant), ultimately becoming its own independent form. And so, it followed the alleluia chronologically, but not necessarily melodically. I would consult Groves for this, which I probably should have done myself before replying!