FLC MISSES CLRNC TO FLY RWY HDG AFTER TKOF.

Narrative

WE WERE CLRED FOR TKOF ON RWY 28 AT GNV AND IT WAS THE FO'S TKOF. THE FO READ BACK THE TKOF CLRNC AND WE COMPLETED THE LINE-UP CHKLIST AND BEGAN THE TKOF ROLL. AT APPROX 400 AGL THE FO MADE A L TURN DIRECT TO THE OCF VOR WHICH IS CUSTOMARY AND I ASKED HIM IF TWR HAD CLRED US DIRECT OCF AND HE SAID WE WERE. TWR SIMULTANEOUSLY SWITCHED US TO ZJX AS WE WERE IN THE TURN. NORMAL CHK IN WITH ZJX TELLING THEM OUR ALT AND THAT WE WERE CLBING TO 2000 FT DIRECT OCF. WE WERE THEN ISSUED A CLB TO 9000 FT. MOMENTS LATER CTR ASKED IF WE HAD BEEN ISSUED RWY HDG BY TWR. I RESPONDED THAT I THOUGHT WE HAD BEEN CLRED DIRECT OCF AND THEN CTR TURNED US R TO 270 DEGS. I ASKED CTR IF I WAS CORRECT IN TURNING DIRECT TO OCF AND THEY SAID TWR HAD CALLED THEM ON THE HDOF AND SAID WE SHOULD BE FLYING RWY HDG. THERE WAS NO TFC CONFLICT. I THINK THE REASON THIS ERROR OCCURRED MY MISSING THE INSTRUCTIONS FROM TWR ON TKOF; AND NOT ASKING TWR WHEN I QUESTIONED THE FO'S LEFT TURN. I FELT AS THIS WAS A VERY SHARP AND EXPERIENCED FO AND DID NOT DOUBT HIM. I AM AN INSTRUCTOR/CHK AIRMAN AND AM VERY USED TO FLYING WITH PLTS THAT ARE NEW TO THE ACFT BUT I HAD LET MY GUARD DOWN FLYING A NORMAL LINE TRIP.