HS125 CREW TOOK OFF FROM RWY 25L AT LAX WITHOUT CLRNC.

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ON APR/FRI/02 I WAS ASSIGNED AS SIC ON A PART 135 PAX FLT; SCHEDULED TO LEAVE LAX AT XA15. I CALLED CLRNC DELIVERY AT ABOUT XZ30 AND RECEIVED OUR CLRNC. I WAS TOLD BY CLRNC TO CONTACT GND ABOUT 2 MINS PRIOR TO ENG START. OUR PAX BOARDED AT ABOUT XA05 AND WE STARTED ENGS TO BE READY TO GO. I CALLED GND CTL AND WAS IMMEDIATELY ADVISED TO CONTACT CLRNC DELIVERY. I CALLED CLRNC AND THEY ADVISED ME THAT WE HAD A WHEELS UP TIME OF 18 PAST THE HR AND ASKED IF WE WOULD BE ABLE TO MAKE THAT TIME. I ADVISED THEM THAT WE WOULD AND THEN TOLD US TO CONTACT GND. I WENT BACK TO GND AND ADVISED THAT WE WERE READY TO TAXI. GND CLRED US TO TAXI TO RWY 25L VIA TXWY A AND HOLD SHORT OF TXWY F. I ACKNOWLEDGED AND WE STARTED OUR TAXI. AS WE TURNED ONTO TXWY A; GND ASKED US TO EXPEDITE OUR TAXI TO TXWY F AND MONITOR TWR. I SWITCHED TO TWR FREQ AND ALMOST IMMEDIATELY THE TWR ASKED 'ARE YOU READY TO GO?' I RESPONDED THAT WE WERE; AND THEY CLRED US INTO 'POS AND HOLD RWY 25L.' I ACKNOWLEDGED AND COMPLETED THE ACFT LINE-UP CHKS. I ALSO MADE A CABIN ANNOUNCEMENT TO THE PAX BECAUSE IT SEEMED THAT WE WERE BEING RUSHED TO DEPART. THIS WAS ALL DONE PRIOR TO REACHING TXWY F. BECAUSE OF THE RUSH AND TRYING TO COMPLETE THE LINE-UP CHKS; I THOUGHT THAT I HEARD 'CLRED FOR TKOF.' I ASKED THE CAPT IF WE WERE CLRED FOR TKOF JUST TO VERIFY IT; AND HE STATED YES. UPON REACHING THE RWY; WE STARTED OUR TKOF ROLL. WHEN THE ACFT REACHED APPROX 40-50 KTS; THE TWR CALLED AND I RESPONDED. THE TWR THEN SAID 'DISREGARD.' WE CONTINUED THE TKOF AND AFTER GETTING AIRBORNE; DEP CTL CALLED AND GAVE US A PHONE NUMBER TO CALL. WE CALLED THE NUMBER AND WERE ADVISED THAT WE HAD TAKEN OFF WITHOUT A CLRNC. I BELIEVE THE THINGS THAT LED UP TO THIS INCIDENT WERE: 1) THE RUSH TO GET US OUT AT OUR ASSIGNED TIME. 2) SEVERAL FREQ CHANGES PRIOR TO TAXI AND DURING TAXI. 3) COMS FROM THE TWR; MAKING IT SOUND AS IF WE NEEDED TO GET AIRBORNE IMMEDIATELY. 4) OUR FAILURE TO VERIFY THAT WE WERE; IN FACT; CLRED FOR TKOF. THE PROB WOULD HAVE BEEN AVOIDED IF I HAD VERIFIED THAT WE WERE OR WERE NOT CLRED FOR TKOF.