The song played to welcome Paulie back ("Paulie's song") is "Nancy (With the Laughing Face)" by Frank Sinatra; it's never explained why it's significant to him.
Песня, играющая при возвращении Поли (песня Поли) - "Nancy (With the Laughing Face" Фрэнка Синатры; почему она важна для него не было объяснено.