B737 pilot reported the aircraft rolled violently left 20 degrees during cruise; followed by a slight Dutch roll.

Narrative

While cruising at FL370 at Mach 0.79; the aircraft violently and aggressively rolled left to approximately 20 degrees of bank within 0.5 seconds. There were no abnormal indications or system alerts at the time of the event. The motion felt as if it originated from the rudder; resembling a yaw-induced roll.I immediately took manual control of the aircraft and stopped the left roll. Following the event; the aircraft exhibited a slight Dutch roll; but it quickly stabilized and returned to normal flight conditions.I immediately called the cabin to check on the status in the back; the flight attendants described it like being hit by a car from the side and said it was violent in nature but reported nobody was up during the incident and everyone appeared to be fine; no further reports from the cabin indicated further issues with aircraft or passengers.I gave control of the aircraft to the first officer so I could look through the QRH and contact dispatch and Maintenance Control. Upon conferencing with Maintenance Control they stated there were no similar entries in the last 60 days. Dispatch said he would continue to monitor the flight should we divert. The first officer and I discussed a plan going forward and being as we were traveling up the east coast with multiple stations and maintenance facilities we continued the flight and continually monitored the aircraft systems the flights landed without further incident and the following logbook entry was made :'At FL370; Mach 0.79; the aircraft violently and aggressively rolled left to approximately 20° of bank within 0.5 seconds.No abnormal indications were present. The movement felt like it originated from the rudder in a yawing motion. I took control of the aircraft and stopped the left roll. The aircraft exhibited a slight Dutch roll after the event but returned to normal flight.There were no reports of turbulence in the area.Weather was clear; with steady and light winds.No aircraft were in the vicinity; so the event is not believed to be associated with wake turbulence.'Environmental Conditions:No reported turbulence in the areaNo significant weather presentWinds were steady and light( no wind shift)No aircraft observed in the vicinity; wake turbulence is not suspected