B757 Captain reported encountering wake turbulence departing LAX in trail of an A320; and stated the spacing seemed abnormally tight.

Narrative

On takeoff from LAX on the ORCA5 departure; we were cleared for takeoff behind an Aircraft Y on the same SID. When we were cleared for takeoff I thought; 'Wow; that guy has just gotten airborne. I haven't been cleared for departure this close behind an aircraft in as long as I can remember!' I then thought; 'Well; the Aircraft Y is smaller than we are; so we should probably be OK.'Shortly after liftoff in IMC; we encountered the Aircraft Y wake turbulence. I had to correct to overcome the rolling tendency; quite a bit actually. A few seconds later; we encountered it again; this time as we were climbing through the tops of the marine layer. We could see the swirling vortex of the wake turbulence in the tops of the clouds and once again; I had to work to overcome the rolling tendency. I thought 'Wow; that would not have been a good thing if we were dealing with an engine failure at the same time; especially during the IMC encounter at the lower altitude!'As we were switched over to Departure frequency; I told Tower about the wake encounter and I think I mentioned how it was a very close proximity between our aircraft departures.