  We continue to consider the ordered lexicographic sequence, which is
constructed according to the formal characteristics of a series of natural
numbers. For analysis, we selected balanced parentheses with zeros, Motzkin
words. As you know, generating functions allow you to work with combinatorial
objects by analytical methods. Motzkin words are enumerated by Motzkin numbers,
for the generation of which there is a corresponding generating function. In
our case, restrictions are imposed on Motzkin words, for example, there are no
leading zeros in bracket sets. The purpose of this article is to obtain the
generating function of such modified Motzkin words.
