Can you tell me the name of this melody?

I'm not really sure how it goes. But it's sad and it's sweet and I
knew it complete, when I wore a younger man's clothes. la la la, di da
da; La la, di di da da dum. Sing us a song, you're the piano man. Sing
us a song tonight. Well, we're all in the mood for a melody-and you've
got us all feelin' all right. Now John at the bar is a friend of mine.
He gets me my drinks for free. And he's quick with a joke and he'll
light up your smoke, but there's some place that he'd rather be. He
says,
"Bill, I believe this is killing me," As his smile ran away from his
face.
"Well I'm sure that I could be a movie star -If I could get out of
this place."
Oh, la la la, di da da; La la, di da da da dum. Now Paul is a real
estate novelist, who never had time for a wife. And he's talkin' with
Davy (who's still in the Navy) and probably will be for life. And the
waitress is practicing politics, as the businessman slowly gets
stoned. Yes, they're sharing a drink they call loneliness.But it's
better than drinkin' alone. Sing us a song you're the piano man. Sing
us a song tonight. Well we're all in the mood for a melody-and you got
us all feeling alright.
It's a pretty good crowd for a Saturday, And the manager gives me a
smile. 'Cause he knows that it's me they've been comin' to see to
forget about their life for a while. And the piano, it sounds like a
carnivore, and the microphone smells like a beer. And they sit at the
bar and put bread in my jar and say, "Man, what are you doin' here?"
Oh, la la la, di da da; La la, di da da da dum.
Sing us a song you're the piano man. Sing us a song tonight. Sell
we're all in the mood for a melody-and you got us all feeling alright.