Consider any sequence consisting of n A's and n B's so that in any of its initial partial segments, the number of B's never exceed the number of A's. It is well known that the number of such sequences is the Catalan number $\frac{1}{n+1}\binom{2n}{n}$.

Now consider sequences consisting of n A's, n B's, and n C's, so that in any initial segments, the number of B's never exceed the number of A's AND the number of C's never exceed the number of B's. Is the number of such sequences known?