B737-300 TAKES OFF WITH PERFORMANCE DATA REFLECTING 12 PAX VICE 112 ACTUALLY ONBOARD.

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WE WERE FLYING FROM LAS. STARTING THE LAST LEG OF THE DAY; WHICH HAD BEEN PROVEN TO BE ONE OF THOSE DAYS WHERE YOU ARE TRYING TO CATCH UP ALL DAY LONG; AND THE DAY BECOMING LONGER AS TIME WENT ON. WE RECEIVED THE LOAD SHEET FROM THE OPS AGENT. THE FO LOADED THE NUMBERS INTO THE OPC AND FMC AS USUAL. I'VE NEVER DONE THIS BEFORE; BUT THIS TIME I FAILED TO COMPARE PLANNED WTS WITH THE ACTUAL WT. I ALSO FAILED TO VERIFY THE PAX COUNT ON THE LOAD SHEET. I HAVE ABSOLUTELY NO EXCUSES!! WE DID; HOWEVER; COMPARE THE LOAD SHEET WITH THE FMC WHICH OBVIOUSLY MATCHED. AT ROTATION; I NOTICED THE ACFT BEING QUITE NOSE HVY; BUT NOTHING THAT UNUSUAL. BEING THAT RWY LENGTH WAS NOT AN ISSUE; I DID WHAT I ALWAYS DO IN SIMILAR NOSE HVY SITUATIONS; I SLOWED DOWN THE ROTATION AND ALLOWED THE ACFT TO FLY OFF ON ITS OWN. THE ACFT FLEW FINE; WITHOUT INCIDENT. HOWEVER; DURING CLBOUT FROM LAS; WE RECEIVED THE MESSAGE FROM OPS OF THE PAX COUNT ERROR. THE LOAD SHEET WAS 100 PEOPLE OFF. OPS MAY HAVE TRIED TO CALL; WHICH WE OBVIOUSLY DID NOT HEAR OR POSSIBLY HAD ALREADY SWITCHED TO TWR. IN MY MIND ONE OF THE MOST DISTURBING THINGS WITH THIS INCIDENT WAS THAT 3 PEOPLE (MYSELF; THE FO; AND OPS AGENT) SHOULD HAVE CAUGHT THE ERROR; BUT DID NOT. I WONDER IF THERE IS A WAY TO HAVE THE GATE READER AUTOMATICALLY INPUT THE NUMBER OF SCANNED BOARDING CARDS ON THE SHEET; WITH THE AGENT MAKING SMALL ADJUSTMENTS. ALSO; PERHAPS OPS COULD UTILIZE ACARS; DISPATCH; OR TWR IF UNABLE TO CONTACT A FLT COMPANY ON RADIO. THE BOTTOM LINE IS THAT THIS RESPONSIBILITY WAS MINE. TIRED OR NOT; I MESSED UP!!! THIS BIG MISTAKE WAS AN EYE-OPENING EXPERIENCE; AND I CAN SAFELY SAY; WILL NEVER HAPPEN AGAIN ON AN AIRPLANE THAT I AM FLYING.SUPPLEMENTAL INFO FROM ACN 692175: WE ENCOUNTERED A LNDG ERROR ON FLT FROM LAS. IT WAS OUR 5TH DAY OF A LONG TRIP. WE ARRIVED IN LAS BEHIND SCHEDULE DUE TO A GND STOP AND WANTED TO GET OUR NEW PAX BACK ON SCHEDULE. WE RECEIVED THE LOAD SHEET FROM OUR OPS AGENT AT THE LAST MINUTE AND I ENTERED THE DATA INTO THE OPC. ACCORDING TO THE LOAD SHEET; THE OPC MATCHED THE FMC WITH REGARDS TO THE TKOF WT AS WELL AS THE FUEL ONBOARD. UNFORTUNATELY; THE ZERO FUEL WT WAS NOT CORRECT ON THE LOAD SHEET. UNFORTUNATELY I ALLOWED MYSELF TO BE RUSHED AND DIDN'T NOTICE THAT THE ZERO FUEL WT JUST DIDN'T MAKE SENSE; ALTHOUGH THE FMC AGREED WITH THE OPC. WE HAD 112 PAX ONBOARD; AND OUR LOAD SHEET REFLECTED 12 PAX. THIS RESULTED IN A DIFFERENCE OF 20000 LBS.