摘要
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 numbers of Dyck paths counted under different conditions, and f（n）, 9（n） and m are functions depending only on about n.
本文通过Cauchy留数定理和算子方法导出了一些形如(?)和(?)的差分恒等式,这里Un,k表示Dyck路在不同条件下的计数公式,f(n),g(n)与m(n)只和n有关的函数.
基金
the "973" Project on Mathematical Mechanizationthe National Science Foundation, the Ministry of Education, and the Ministry of Science and Technology of China.
