Consider a combination lock consisting of buttons that can be pressed in any combination (including
multiple buttons at once), but in such a way that each number is pressed exactly
once. Then the number of possible combination locks with buttons is given by the number of lists
(i.e., ordered sets) of disjointnonemptysubsets of the set that contain each number exactly once. For example,
there are three possible combination locks with two buttons: , , and . Similarly there are 13 possible three-button combination
locks: ,
, , , , , , , , , , , .

Sloane, N. J. A. Sequence A000670/M2952 in "The On-Line Encyclopedia of Integer Sequences."Velleman,
D. J. and Call, G. S. "Permutations and Combination Locks." Math.
Mag.68, 243-253, 1995.