Ah, yes, thanks. Wikipedia writes:

*
A **k*-combination with repetitions, or *k*-multicombination, or multisubset of size *k* from a set *S* is given by a sequence of *k* not necessarily distinct elements of *S*, where order is not taken into account: two sequences of which one can be obtained from the other by permuting the terms define the same multiset. In other words, the number of ways to sample *k* elements from a set of *n* elements allowing for duplicates (i.e., with replacement) but disregarding different orderings (e.g. {2,1,2} = {1,2,2}).

So it seems that they're called "multicombinations" or "multisubsets", and I wasn't too far off the mark when talking about multisets.

Comment onRe^6: Faster alternative to Math::Combinatorics