COMMUTER ACFT DEPARTS WITH UNUSABLE PAX SEAT OCCUPIED.

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I AM A CAPT OF A 19 SEAT COMMUTER AIRPLANE. THE PARTICULAR AIRPLANE I WAS TO FLY HAD ONLY 18 SEATS AVAILABLE BECAUSE 1 SEAT WAS IN NEED OF REPAIR; AND WAS PLACARDED UNUSABLE. AT MY AIRLINE; THE CAPT DOES THE ENTIRE MANIFEST IN THE COCKPIT; AFTER THE R ENG HAS BEEN STARTED; IN ORDER TO EXPEDITE THE DEP. WHILE FIGURING THE MANIFEST; I BECAME INVOLVED IN A CONVERSATION WITH ONE OF THE BAGGAGE HANDLERS AS TO THE WT DISTRIBUTION LIMITS IN THE AFT CARGO COMPARTMENTS. THIS EXCHANGE WAS DELAYING OUR GATE DEP. THE FO WAS BUSY GIVING THE REQUIRED SAFETY BRIEFING TO THE PAX. I DID NOT NOTICE THAT 19 PAX HAD BEEN BOARDED AND SEATED. I QUICKLY COMPLETED THE MANIFEST AND DEPARTED THE GATE. I HAD COMPLETELY FORGOTTEN THAT 1 SEAT WAS PLACARDED UNUSABLE UNTIL AFTER THE FLT HAD BEEN COMPLETED. EVIDENTLY; THE PERSON WHO SAT IN THE SEAT WITH 'DO NOT OCCUPY' IN VERY LARGE LETTERS FOUND IT USABLE ENOUGH. THE LESSONS TO BE LEARNED FROM THIS INCIDENT ARE NOT NEW ONES TO MOST PROFESSIONAL PLTS: IF I HAD NOT BEEN SO PREOCCUPIED WITH THE AFT CARGO LOADING; AND IF I HAD NOT BEEN SO PREOCCUPIED WITH THE AFT CARGO LOADING; AND IF I HAD NOT RUSHED TO COMPLETE THE MANIFEST IN ORDER TO STAY ON SCHEDULE; I WOULD HAVE SEEN THAT I RECORDED 19 PAX ON THE MANIFEST. ALSO; A CONTRIBUTING FACTOR IN THIS INCIDENT WAS SOME MEASURE OF MENTAL FATIGUE DUE TO A LACK OF SUFFICIENT SLEEP FROM A REDUCED REST PERIOD THE PREVIOUS NIGHT.