{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:35:43Z","timestamp":1760236543924,"version":"build-2065373602"},"reference-count":28,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2021,12,1]],"date-time":"2021-12-01T00:00:00Z","timestamp":1638316800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In this paper, we perform a further investigation for the Catalan numbers. By making use of the method of derivatives and some properties of the Bell polynomials, we establish two new expressions for sums of products of arbitrary number of the Catalan numbers. The results presented here can be regarded as the development of some known formulas.<\/jats:p>","DOI":"10.3390\/axioms10040330","type":"journal-article","created":{"date-parts":[[2021,12,1]],"date-time":"2021-12-01T05:02:36Z","timestamp":1638334956000},"page":"330","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["New Expressions for Sums of Products of the Catalan Numbers"],"prefix":"10.3390","volume":"10","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4869-5537","authenticated-orcid":false,"given":"Conghui","family":"Xie","sequence":"first","affiliation":[{"name":"College of Information Science and Technology\/College of Cyber Security, Jinan University, Guangzhou 510632, China"},{"name":"Faculty of Science, Kunming University of Science and Technology, Kunming 650500, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3392-2338","authenticated-orcid":false,"given":"Yuan","family":"He","sequence":"additional","affiliation":[{"name":"School of Mathematics and Information Science, Neijiang Normal University, Neijiang 641100, China"}]}],"member":"1968","published-online":{"date-parts":[[2021,12,1]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"267","DOI":"10.1016\/0097-3165(87)90033-1","article-title":"Catalan numbers, q-Catalan numbers and hypergeometric series","volume":"44","author":"Andrews","year":"1987","journal-title":"J. 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