Chapter 8.1, Problem 6E

a) Find a recurrence relation for the number of strictly increasing sequences of positive integers that have 1 as their first term and n as their last term, where n is a positive integer. That is, sequences $a_1,a_2,\mathrm{...},a_k$, where $a_1=1,a_k=n$ ,and $a_j<a_{j+1}$ for $j=1,2,\mathrm{...},k-1$ .

b) What are the initial conditions?

c) How many sequences of the type described in (a) are there when n is an integer with $n\ge 2$ ?