E145 EXPERIENCES ENG FAILURE AT FL370. MAKES CTLED DSCNT AND LNDG AT A DIVERSION ARPT.

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WHILE IN CRUISE FLT AT FL370; THE #1 ENG FAILED. WE WERE IN CRUISE AT THIS ALT FOR OVER 30 MINS AND THE AIR WAS SMOOTH WITH OCCASIONAL LIGHT TURB SO THE SEATBELT SIGN WAS ON. I NOTICED A YAWING AND A DECREASE IN ENG SOUND FOLLOWED BY CAUTION BELLS AND LIGHTS AND IMMEDIATELY DISENGAGED THE AUTOPLT AND TRIMMED FOR SINGLE ENG FLT WHILE BEGINNING THE MEMORY ITEMS FOR ENG FAILURE. I HAD THE FO DECLARE AN EMER AND WE WERE GIVEN ALT AT OUR DISCRETION AND I BEGAN A SHALLOW DSCNT. WE HAD JUST FLOWN OVER ZZZZ AND CTR INFORMED US THAT IT WAS OUR CLOSEST ARPT; SO I MADE A SHALLOW TURN BACK TOWARDS ZZZZ. AT THIS TIME; THE FO WAS GOING THROUGH THE EPC AND I CALLED THE FLT ATTENDANT AND ASKED IF THERE WAS ANY SMOKE OR UNUSUAL NOISE OR VIBRATION IN THE REAR OF THE ACFT. SHE DID NOT NOTICE ANYTHING AND WAS ACTUALLY IN THE REAR OF THE ACFT WHEN THE FAILURE OCCURRED. I INFORMED THE FLT ATTENDANT OF THE EVAC ITEMS GIVING HER APPROX 10 MINS BEFORE LNDG WITH NO PLANNED EVAC. THE PAX WERE CALM AND EXPECTED A NORMAL LNDG AFTER BEING INFORMED OF OUR CONDITION THROUGH A PA. DURING THE DSCNT; BELOW FL250; WE GOT TO THE PART OF THE CHKLIST ASKING FOR A RESTART AND NOTING NOTHING THAT WOULD PROHIBIT AN ATTEMPT; FO ATTEMPTED A START AND IT WAS UNSUCCESSFUL. WE TRIED AN APU STAT AND IT WAS UNSUCCESSFUL AS WELL; BUT WHEN WE DSNDED BELOW FL180 ANOTHER ATTEMPT WAS MADE AND THE APU STARTED. THE SHALLOW DSCNT NECESSITATED SEVERAL SHALLOW 360 DEG TURNS TO GET DOWN; BUT I WANTED THE ALT AND TIME TO RUN THE CHKLIST SO WE WERE FAIRLY HIGH CLOSE TO THE ARPT BUT GOT INTO POS WELL FOR THE DSCNT AND LNDG. THE CONDITIONS AT CRUISE ALT WERE VMC AND WE WENT THROUGH A FEW THOUSAND FT OF IMC BUT ZZZZ WAS CLR. I REQUESTED THE CFR EQUIP BE STANDING BY AND WE MADE A NORMAL SINGLE ENG APCH AND LNDG. I STOPPED ON THE RWY AND HAD THE TRUCKS COME AND LOOK AT OUR ENG AND THEY DETERMINED IT WAS NOT DAMAGED FROM THE OUTSIDE AND NOTHING WAS LEAKING SO I TAXIED TO THE GATE WITH A TRUCK FOLLOWING ME. WE DEPLANED THE PAX NORMALLY AND THEY CONNECTED TO ANOTHER FLT WHILE WE TALKED TO DISPATCH; THE CHIEF PLT AND MAINT CTL. THERE WAS A CONTRACT MECH ON THE ACFT AT THIS TIME AND WE INFORMED HIM OF WHAT HAD HAPPENED AS WELL.