Medium Transport; High Wing; 2 Turboprop Eng
Air Traffic Control Fully Certified
Air Traffic Control Time Certified In Pos 1 (yrs) 7
Situational Awareness; Fatigue; Confusion; Time Pressure
ATC Issue All Types; Conflict Airborne Conflict; Deviation / Discrepancy - Procedural Published Material / Policy; Ground Incursion Runway
Human Factors; Procedure
I cleared Aircraft X for takeoff RWY 10R at intersection E; heading 110.  Problem is that I had forgotten about Aircraft Y on landing roll. Aircraft X didn't say anything; but waited for Aircraft Y to exit; then departed. I realized what had happened when Aircraft Y was exiting.  I didn't stop Aircraft X because it wouldn't have mattered at that point. Those pilots had my back. Thankfully their scan was better than mine.I was looking into the sun so the visibility in that direction wasn't ideal; but if I had been more intentional with my scan; this wouldn't have happened.  I must have not scanned the ASDE; because then I'm sure I would have seen the small transport.  The previous night my sleep was interrupted from about 1-4 a.m. I didn't really feel the effects at the time of the incident; but in hindsight I wasn't as sharp as normal. Later in the shift I felt very tired.
PDX Local Controller doesn't cancel takeoff clearance to departing aircraft while previous arrival is still on runway.