An illustration for  A187783, the array that shows the number of possible permutations of these multisets
These multisets have the signatures  A249543(m,n-1) for m&gt;=1 and n&gt;=2, i.e. they correspond to the integer partitions denoted by these numbers.
The multisets in column 1 for m&gt;=1 have signature 0. For empty sets the concept of a signature does not really make sense.
Own work
WatchduckYou can name the author as "T. Piesk", "Tilman Piesk" or "Watchduck".