The children's series SESAME STREET/PBS/1969+ was inspired by the
very same phrase. The term "Sesame" was chosen with the hopes that
the program would "open up" the minds of the children who viewed the
series.
One day, when Ali Baba was in the forest, he saw a troop of men on
horseback, coming toward him in a cloud of dust. He was afraid they
were robbers, and climbed into a tree for safety. When they came up
to him and dismounted, he counted forty of them. They unbridled
their horses and tied them to trees.
The finest man among them, whom Ali Baba took to be their captain,
went a little way among some bushes, and said, "Open, Sesame!" so
plainly that Ali Baba heard him.
A door opened in the rocks, and having made the troop go in, he
followed them, and the door shut again of itself. They stayed some
time inside, and Ali Baba, fearing they might come out and catch
him, was forced to sit patiently in the tree. At last the door
opened again, and the Forty Thieves came out. As the Captain went in
last he came out first, and made them all pass by him; he then
closed the door, saying, "Shut, Sesame!"
Every man bridled his horse and mounted, the Captain put himself at
their head, and they returned as they came.
Then Ali Baba climbed down and went to the door concealed among the
bushes, and said, "Open, Sesame!" and it flew open.
Ali Baba, who expected a dull, dismal place, was greatly surprised
to find it large and well lighted, hollowed by the hand of man in
the form of a vault, which received the light from an opening in the
ceiling. He saw rich bales of merchandise -- silk, stuff-brocades,
all piled together, and gold and silver in heaps, and money in
leather purses. He went in and the door shut behind him. He did not
look at the silver, but brought out as many bags of gold as he
thought his asses, which were browsing outside, could carry, loaded
them with the bags, and hid it all with fagots.
Using the words, "Shut, Sesame!" he closed the door and went home.