The powers of a function f: A → A are defined recursively byFor n ≥ 1, let an denote the n...

The powers of a function f: A → A are defined recursively by

For n ≥ 1, let an denote the number of ways to express n as the sum of natural numbers, taking order into account. For example, 3 = 1 + 1 + 1 =2 + 1 = 1 + 2, so a3 = 4.

(a) [BB] Find the first five terms of the sequence {an}.

(b) Guess and then establish a formula for an.