Algorithm for creating n-multiset out of x?
Every such arrangement of 15 balls to 21 boxes corresponds, in a one-to-one fashion, to a string of the form *|**||||...|*, where there are a total of 35 symbols in the string, exactly 15 stars and 20 bars.  (Think of each * as a ball, and each | as a divider between two boxes.)  These, in turn, correspond to the set of binary strings of length 35 that contain exactly 20 one's, which in turn corresponds to the set of ways to choose a subset of 20 positions out of a set of 35 possibilities.

It follows that you can enumerate the set of valid nodes by enumerating all ways to choose a subset of size 20 that's contained in $\{1,2,\dots,35\}$.  There are standard ways to perform this enumeration.  One way is to use the combinatorial number system, which creates a correspondence between these subsets and integers in the range $\{1,2,\dots,{35 \choose 20}\}$.  See also https://en.wikipedia.org/wiki/Combination#Enumerating_k-combinations, Get a fixed-size family of k-element subsets, https://cs.stackexchange.com/a/72543/755 for more.