EMB ERJ 170/175 ER/LR
Flight Crew Air Transport Pilot (ATP); Flight Crew Instrument; Flight Crew Multiengine
Flight Crew Total 2000; Flight Crew Type 500
Situational Awareness
Deviation - Speed All Types; Inflight Event / Encounter CFTT / CFIT; Inflight Event / Encounter Wake Vortex Encounter
Flight Crew FLC complied w / Automation / Advisory
Equipment / Tooling; Procedure; Environment - Non Weather Related
Las Vegas Ground assigned us Runway 26R.  We were cleared for takeoff; provided we had visual separation with an A321 and we did have visual separation.  Our takeoff data called for a Flaps 1 takeoff; which requires a slightly longer takeoff roll.  After the takeoff roll on [Runway] 26R; I was hand flying the aircraft during the initial climb.  At about 500 ft. AGL; we encountered wake turbulence from the A321.  This is what caused the stick shaker to activate.  I immediately stated; 'Stall'; and pitched the nose of the aircraft down; announced 'Max Thrust' and applied Max Thrust by pushing the thrust levers past their detents.  We regained speed almost immediately but due to the nose down pitch to recover from the stall; we received an EGPWS warning.  We received this EGPWS warning as I was pitching back up to continue our climb after the stall recovery.  The EGPWS warning did not last more than one auditory message and it was gone.  We advised Las Vegas Tower of the situation and were then transferred to Las Vegas Approach; where we continued the remainder of the flight without incident.  In the end; we believe we only lost about 100 feet from the stall recovery before continuing our climb on the departure.  After looking back; there are two things in my mind that possibly could have helped.  One would be to have re-sent for the takeoff data to get a flaps 2 takeoff; which would have allowed us to have a shorter takeoff roll.  However; there was no way of knowing we would encounter the wake of another aircraft and had no reason to believe a flaps 1 takeoff would not suffice.  The second thing I think that could have helped was to delay our takeoff roll slightly for about 15-30 more seconds to have a bit more separation from the other aircraft.  At the end of the day the stall recovery procedure was performed by the standards it is trained and the flight was completed without injury or incident.
EMB-175 First Officer reported a wake turbulence encounter climbing out of 500 feet AGL departing LAS in trail of an A321 that resulted in a stick shaker and an uncommanded descent that triggered an EGPWS warning.