In this paper we consider the enumeration of subsets of the set, say Dm, of those Dyck paths of arbitrary length with maximum peak height equal to m and having a strictly increasing sequence of peak height (as one go...
the "973" Project on Mathematical Mechanizationthe National Science Foundation, the Ministry of Education, and the Ministry of Science and Technology of China.
In the paper we derive many identities of forms ∑i=0^n(-1)^n-i(i^n)Um+k+i,k+i=f(n)and ∑ i=o^2n(-1)^i(i^2n)Um+k+i,k+i=9(n)by the Cauchy Residue Theorem and an operator method, where Un, k are number...