A320 TAKES OFF FROM DEN AFTER ACCEPTING CLRNC FOR ANOTHER ACFT.

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DURING GND OPS; I EXPECTED AND PLANNED FOR A TKOF ON RWY 8. OUR TAXI CLRNC FROM RAMP WAS TO TAXI W FROM GATE TO 3W. THIS MEANT A VERY SHORT TAXI TO A TKOF ON EITHER RWYS 34R; 34L; OR 25. I CHOSE RWY 34R AND DID ALL THE PERFORMANCE AND LOADED THE FMGC AGAIN. WE THEN SPOKE TO GND AND WERE TOLD TO EXPECT RWY 34L. AGAIN; I SENT FOR THE PERFORMANCE AND LOADED THE FMGC. I THEN INFORMED THE CAPT I WAS HEADS DOWN; NEEDED MORE TIME; AND WAS BEHIND. TO THE CAPT'S CREDIT; HE ASSURED ME TO TAKE ALL THE TIME I NEEDED AND NOT TO RUSH. DURING THIS TIME; TWR CLRED US FOR TKOF ON RWY 34L; AT WHICH POINT THE CAPT INFORMED THEM WE NEEDED MORE TIME. THEY CANCELLED OUR TKOF CLRNC AND TOLD US TO FINISH OUR CHKS ON D2. I FINISHED ALL THE CHKS AND INFORMED THE CAPT. THEN I THOUGHT I HEARD OUR TKOF CLRNC FOR RWY 34L. THE CAPT ACTUALLY READ BACK THE TKOF CLRNC TO TWR; TAXIED THE ACFT ONTO THE RWY; SAID 'YOUR THROTTLES' DURING THE TURN AND THEN XMITTED TO TWR; 'CONFIRM ACR X IS CLRED FOR TKOF?' TWR THEN STARTED TO SPEAK WITH ANOTHER ACFT. I THEN SAID; 'I HEARD THE CLRNC' AND HE SAID 'OK' AND I CONTINUED THE TKOF. AFTER LIFTOFF; TWR ASKED WHERE WE WERE; AND INFORMED US THAT THEY CLRED ACR Y FOR TKOF. NO CONFLICT WAS EVIDENT TO US AND NO AVOIDANCE VECTORS WERE ISSUED THAT I HEARD. HUMAN FACTORS: THIS WAS THE 4TH LEG OF THE DAY AND THIRD ACFT CHANGE. I FINISHED A320 TRANSITION IN MARCH AND IOE IN APRIL. I HAD NEVER FLOWN 4 LEGS IN 1 DAY IN MY CAREER. WITHOUT A DOUBT I WAS TIRED; BUT I FELT I WAS FIT TO FLY. LOOKING BACK ON IT; I SHOULD HAVE STOPPED THE TKOF ROLL (VERY LOW SPD) AND LET THE CAPT SORT OUT THE CLRNC WITH TWR. I ALSO FEEL TWR SHOULD HAVE PAID ATTN TO THE CAPT'S READBACK; ESPECIALLY SINCE IT WAS NOT BUSY. SUPPLEMENTAL INFO FROM ACN 616612: AS WE ROLLED INTO POS; I QUERIED TWR TO CONFIRM WE WERE CLRED FOR TKOF AS I THOUGHT IT ODD THAT HE SOMEHOW KNEW WE WERE READY. I ALSO QUERIED BECAUSE AS WE STARTED TKOF I NOTICED AN RJ PULLING UP TO HOLD SHORT. THE COPLT THEN CONFIRMED HE HEARD THE TKOF CLRNC FOR US. JUST BEFORE ROTATION TWR SAID 'WHERE ARE YOU?' AT 1000 FT; I TOLD TWR WE WERE AIRBORNE. CTLR STARTED RANTING ABOUT HOW HE NEVER GAVE US CLRNC FOR TKOF. I SHOULD HAVE PREVAILED WITH MY QUERY AND GOT THE CONFIRMATION FROM TWR. I WAS EASILY SWAYED BY THE COPLT CONFIRMING THE CLRNC.