AN A300 PIC FORGETS TO SHUTDOWN THE #2 ENG AFTER SHUTTING THE #1 ENG DOWN AT THE GATE AT JFK; NY.

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LOCATION: JFK GATE. I REMEMBER WAITING FOR 5 MINS TO PARK AT GATE. I REMEMBER SETTING THE PARKING BRAKES AND TURNING OFF THE SEATBELT SIGN AND THEN LOOKING AT THE APU AVAIL LIGHT AND THINKING WE HAVE PWR BUT NO AIR DUE TO APU INOP; SO I SAID 'SHUT 'EM DOWN.' THE FO MUST HAVE HEARD 'SHUT ONE DOWN.' I REMEMBER LOOKING AT THE FUEL FLOW GAUGES BUT DID NOT FOCUS ON THE FACT THAT ONLY 1 NEEDLE JUMPED TO ZERO. I THEN THOUGHT THE HIGH FANS SHOULD BE COMING ON SINCE WE HAVE NO BLEED AIR. I THEN GOT DISTR WITH THE COMPLETION FO THE CHKLIST AND DID NOT GO BACK AND RECHK THE ACCOMPLISHMENT OF THE CHKLIST. CORRECTIVE ACTION: I WILL PHYSICALLY PLACE MY HANDS ON THE FUEL LEVERS AFTER THEY HAVE BEEN TURNED OFF. I WILL ALSO RESTATE THE ACCOMPLISHMENT OF THE FIRST 4 ITEMS AFTER THEY ARE COMPLETE. THERE IS NO EXCUSE BUT A CONTRIBUTING REASON MAY HAVE BEEN FATIGUE AS I HAD BEEN UP 18 HRS -- EVEN THOUGH ON DUTY LESS THAN 10 HRS. THE IMPORTANCE OF CHKLIST DISCIPLINE CANNOT BE OVERSTATED. I WILL RE-EMPHASIZE THE FIRST 4 ITEMS AS A DO LIST THEN BACK IT UP WITH A CHKLIST AND READ/RESPOND AFTER THE ITEMS HAVE BEEN ACCOMPLISHED.