In this paper, we define sequence dominated by 0, in which every initial fragment contains more zeroes than ones. If n ≥ 2 · m and n > 0, then the number of sequences dominated by 0 the length n including m of ones, is given by the formula
and satisfies the recurrence relation
Obviously, if n = 2 · m, then we obtain the recurrence relation for the Catalan numbers (starting from 0)
Using the above recurrence relation we can see that
where and hence
MML identifier: CATALAN2, version: 7.8.03 4.75.958