| Identities Involoving Some Numbers Related to Dyck Paths |
| Received:June 23, 2003 |
| Key Words:
Identities Dyck path Catalan numbers Motzkin numbers
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| Fund Project:the "973" Project on Mathematical Mechanization, the National Science Foundation, the Ministry of Education, and the Ministry of Science and Technology of China. |
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| Abstract: |
| In the paper we derive many identities of forms ∑i=0n (-1)n-i(n i)Um+k+i, k+i =f(n) and ∑i=02n(-1 )i(2n i) Um+k+i, k+i = g(n) by the Cauchy Residue Theorem and an operator method, where Un, κ are numbers of Dyck paths counted under different conditions, and f(n), g(n) and m are functions depending only on about n. |
| Citation: |
| DOI:10.3770/j.issn:1000-341X.2005.03.009 |
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