Find all combinations of size at least k to n

I am struggling to figure out the formula to solve this problem:

Given an array of nnumbers and a limit k, count all distinct combinations of at least size .k

E.g:A=[1,2,3] k = 2 output = 4 // [1,2],[1,3],[1,2,3],[2,3]

• The array can contain repeated numbers.

For example: A=[1,1,2] k = 2 output = 3 // [1,1],[1,2],[1,1,2]but [1,2],[2,1], etc.not accepted.

I can use backtrackingTLE to solve it . I've been trying to find a formula from a question like all combinations nfound or all combinations of sizes found kwithout success.

So far I have figured out this table:

row = k
col = n
   1 2 3 4 5
  ---------
1| 1 2 3 4 5
2|   1 3 6 10
3|     1 4 10
4|       1 5 

The formula (not what I want) is:

combinations of size i with j numbers:
dp[i][j] = dp[i][j-1] + dp[i-1][j-1]

count(n,k) combinations of size k with n numbers
count(2,1) = 2
count(4,3) = count(3,3) + count(3,2) = 1 + 3 = 4
count(5,2) = count(4,2) + count(4,1) = 6 + 4 = 10
and so on

Even pseudocode would be greatly appreciated.

Update: Based on Oliver Dain's answer, if you're interested, use the following code

def count_combinations(n, k):
    count = 0
    for i in range(k, n + 1):
        count += math.factorial(n)/(math.factorial(i)*math.factorial(n - i))
    return int(count)