Subalgebras of a Finite Monadic Boolean Algebra

For a finite n-element set X, n ≥ 1, let N [X] denote the number of elements of X and let p(n) denote the number of all partitions of X. If Bn is a Boolean algebra with n atoms, let A(Bn) be the set of all atoms of Bn. It is known that there exists a bijective correspondence between the set S(Bn) of all subalgebras of Bn and the set of all partitions of A(Bn), i.e., N [S(Bn)] = p(n). The following recursive formula for p(n) can be found in [5]: if we define p(0) = 1, then