B737-300 FLT CREW REPORTS OMITTING THE SID TRANSITION AFTER A RWY CHANGE REQUIRES THE SID TO BE REENTERED IN THE FMC. ERROR IS CORRECTED BY ATC.

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WE WERE EXPECTING A DIFFERENT RWY WHILE AT THE GATE. FMC WAS LOADED WITH RTE AS PLANNED. UPON TAXI WE WERE ASSIGNED RWY 18L; WHICH WAS NOT THE RWY IN FMC. MY FO HAD LOTS OF EXPERIENCE AND INFORMED ME THAT HE WOULD BE HEADS DOWN WHILE I TAXIED TO CHANGE RWY DEP; TRANSITION; AND PERFORMANCE DATA. I SAID IT WAS OK AND THAT I DIDN'T HAVE TO HAVE HIM HELP WITH TAXI INSTRUCTIONS. WE WERE #1 FOR TKOF AND HE SAID HE GOT IT ALL DONE AND I FELT COMFORTABLE WITH HIS STATEMENT; SO WE DID BEFORE TKOF CHKLIST AND WAS CLRED FOR TKOF. UPON DEPARTING BLECO FIX THE TRANSITION SHOULD HAVE TAKEN US TO ZEMMR INSTEAD WE WENT DIRECT TO IRW. THE CTLR QUERIED US AND WE REALIZED THAT THE FMC MUST NOT HAVE BEEN PROGRAMMED CORRECTLY WITH THE TRANSITION. I FEEL THAT IF RWYS WERE ASSIGNED BEFORE DEP FROM THE GATE WITH THE ATC CLRNC IT WOULD ALLEVIATE A MULTITUDE OF PROBS ESPECIALLY WITH RWY SPECIFIC-RNAV DEPS. NO CONFLICTS WITH TFC OCCURRED. SUPPLEMENTAL INFO FROM ACN 761492: BEFORE DEP WE RECEIVED A NEW RWY (RWY 18L VERSUS RWY 17R) I CHANGED THE SELECTED NEW RWY; RESELECTED THE SID BUT SINCE IT WAS THE SAME TRANSITION; DID NOT RESELECT THE TRANSITION. BY NOT DOING THAT; THE FMC RTE APPEARED BLECO-IRW. THE CORRECT RTE PER THE TRANSITION WAS BLECO-ZEMMR-IRW. AFTER BLECO WE PROCEEDED DIRECT TO IRW. WE WERE QUESTIONED BY ATC WHO THEN GAVE US A RADAR VECTOR TO AVOID AN ACTIVE MOA. SHORTLY AFTER WE WERE GIVEN DIRECT IRW. NO FURTHER INCIDENT.