{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:35Z","timestamp":1753893815223,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>In this paper, we prove the following result conjectured by Z.-W. Sun:$$(2n-1){3n\\choose n}|\\sum_{k=0}^{n}{6k\\choose 3k}{3k\\choose k}{6(n-k)\\choose 3(n-k)}{3(n-k)\\choose n-k}$$by showing that the left-hand side divides each summand on the right-hand side.<\/jats:p>","DOI":"10.37236\/3100","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T01:12:37Z","timestamp":1578705157000},"source":"Crossref","is-referenced-by-count":4,"title":["Proof of Sun's Conjecture on the Divisibility of Certain Binomial Sums"],"prefix":"10.37236","volume":"20","author":[{"given":"Victor J. W.","family":"Guo","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2013,11,22]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v20i4p20\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v20i4p20\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T11:10:56Z","timestamp":1579259456000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v20i4p20"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,11,22]]},"references-count":0,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2013,10,14]]}},"URL":"https:\/\/doi.org\/10.37236\/3100","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2013,11,22]]},"article-number":"P20"}}