
A Combinatorial Interpretation of the Numbers 6 (2n)!/n!(n + 2)!
... given in the next section. Lemma 2.1. For n ≥ 1, Cn equals the number of pairs of Dyck paths (P, Q) of total semilength n, with P nonempty and h(P ) ≤ h(Q) + 1. Proof. Let Dn be the set of Dyck paths of semilength n, and let En be the set of pairs of Dyck paths (P, Q) of total semilength n, with P n ...
... given in the next section. Lemma 2.1. For n ≥ 1, Cn equals the number of pairs of Dyck paths (P, Q) of total semilength n, with P nonempty and h(P ) ≤ h(Q) + 1. Proof. Let Dn be the set of Dyck paths of semilength n, and let En be the set of pairs of Dyck paths (P, Q) of total semilength n, with P n ...