Program that should output nth arrangement of paintings
I have thought of the following algorithm that is NOT recursive at all and thus has linear \$o(n)\$ complexity (n being the total number of works meaning a+b+c+d+e...):

The order of arrangements in the list is alphabetical.  This means that the list will forever begin with arrangements beginning with A and then arrangements beginning with B and so on. So looking at the example list in the question, the first column of letters shows consecutive ranges of letters: AAABBBBBBCCC. You can calculate this "list of first letters" based on the input values of how many artists and how many works for each artist (I will let you figure out the exact formula, its pretty easy). So now you can determine the first letter of the nth arrangement directly from this formula.  

Once you have that, it's pretty easy to calculate the rest of the letters by removing the first letter and applying the formula as if the input was one work less.