Let r_n,k denote the number of ways to divide n people into k groups, with at least two people in each group. For example, r_4,2= 3. Set r_0,0=1

a) Use a combinatorial argument to show that r_n,k satisfies the recurrence relation r_n,k = kr_n-1,k + (n-1)r_n-2,k-1 for n1

b) Define r_n for n 0 by r_n = krn,k Compute the table of values of r_n,k and r_n for 0n8

c) Determine a formula for r_2n,n, for a positive integer n