This is a variation of question asked on this site before.
Consider a set with $𝑎_1$ 'distinct' 1s, $𝑎_2$ 'distinct' 2s, ... , $𝑎_𝑛$ 'distinct' ns. You have $𝑎_1+1$ choices for the 1s (including the option of none of them being chosen) and similarly for the other elements. The total number of subsets is therefore $(𝑎_1+1)(𝑎_2+2)...(𝑎_𝑛+1)$
Now how to find the number of subsets with size $\leq $ 'k'.