Elementary results in combinatorics show that Dyck words are in bijection with hundreds of combinatorial structures (well balanced parentheses word, binary trees, lattice paths, polygon triangulations...) and the number d(2n) of Dyck word of length 2n is the n-th Catalan number : binomial(2n,n)/(n+1).
A shuffle of two words is defined recursively as follows :
for any letters a,b, for any word u,v,
a.u shuffle b.v := a. (u shuffle b.v) union b.(a.u shuffle v).
u shuffle 1 = 1 shuffle u := u.
Now, the shuffle C of two languages A and B is the set C:={w=u shuffle v | u in A, v in B}.