My basic intuition to solve this problem is by using permutation and combination.
Example-
n=2,k=2
5c1 * 21c1 + 21c1 * 5c1 + 21c1*21c1 + 5c1 * 5c1
Am I going to right direction or not?

n=1,k=1
21c1 +5c1=26

Please do provide code too.