This is the title sequence for The Roman Holidays, a Hanna-Barbera Productions cartoon that lasted for 13 episodes in 1972. It was quite similar to The Flintstones which itself was inspired by The Honeymooners. From Toonopedia:
The show's title came from the setting (ancient Rome) and the protagonists' family name (Holiday, which was just ever so typical a family name back then). Dad's first name was Gus and Mom's was Laurie. They had a teenage daughter named Groovia, an in-house son-in-law named Happius (usually called Happy) and a younger daughter named Precocia. Their pet cat, Brutus (no relation), was actually a lion. Like modern nuclear family heads, Gus went to work every day, where his boss was Mr. Tycoonus, and came home each night to the Venus de Milo Arms, where his landlord was Mr. Evictus (Dom DeLuise! -ed.).