President Trump & Melania's First Dance

President Donald Trump & First Lady Melania Trump just shared their first dance ... and did it their way.

They hit the dance floor to Frank Sinatra's "My Way" at Friday's Liberty Ball courtesy of Nashville based singers Erin Boehme, Nickie Conley and Jason Eskridge belted the tune.

As the song went on, they were joined by Mike Pence and his wife ... and then more and more of their family members ... we're told it was a totally organic moment.

Trump's got a busy night ahead -- starting at the Liberty and Freedom Balls at the Walter E. Washington Convention Center -- before heading to The Salute To Our Armed Services Ball down the street.

Scheduled performers were The Radio City Rockettes, Sam Moore and The Piano Guys.

Talk about a long day.