One Thousand and One Nights vs Thousand and One Nights

One Thousand and One Nights and Thousand and One Nights both are nouns.

Word	Noun	Adjective	Verb	Adverb
One Thousand and One Nights	Yes	No	No	No
Thousand and One Nights	Yes	No	No	No

As nouns, One Thousand and One Nights and Thousand and One Nights are synonyms defined as:

One Thousand and One Nights and Thousand and One Nights: a collection of folktales in Arabic dating from the 10th century

Other synonyms of One Thousand and One Nights include Arabian Nights' Entertainment, Arabian Nights.

One Thousand and One Nights (noun)	Thousand and One Nights (noun)
a collection of folktales in Arabic dating from the 10th century	a collection of folktales in Arabic dating from the 10th century