This project contains a small C# application that uses available processors, a large internal memory cache and BigInteger to compute how many multiplicity sequences there are for any given sum of multiplicities in the sequence.
You can find some results in the Results folder. Here you can find the number of multiplicity sequences there are, for all multiplicity sequences with a multiplicity sum up to and including 10'000. (There are 36167251325636293988820471890953695495016030339315650422081868605887952568754066420592310556052906916435144 multiplicity sequences having a multiplicity sum of 10'000).