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 a1, , where a1 = 1, ak = n, and aj < aj+1 for j = 1, − 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 ≥ 2?