Lean-to-shelter radical wrapping the upper-left — the indexing radical, picturing a roof with one side open to the wall. It marks 序 as something belonging to a building: the side-walls of a hall, where guests were seated in order of rank. Same radical heads 庭 (courtyard), 庙 (temple), 床 (bed).
Inside 予 supplies the sound (yǔ → xù with a y/x palatalisation). 予 originally pictured two hands passing an object, and that 'giving in turn' image is a faint semantic bonus: a sequence is one thing handed to the next. Same phonetic seeds 预 (in advance), 抒 (express), 舒 (relaxed).
