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...
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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.
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