{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,13]],"date-time":"2026-02-13T10:29:29Z","timestamp":1770978569588,"version":"3.50.1"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>In this paper we study products and sums divisible by central binomial coefficients. We show that $$2(2n+1)\\binom{2n}n\\ \\bigg|\\ \\binom{6n}{3n}\\binom{3n}n\\ \\ \\mbox{for all}\\ n=1,2,3,\\ldots.$$ Also, for any nonnegative integers $k$ and $n$ we have $$\\binom {2k}k\\ \\bigg|\\ \\binom{4n+2k+2}{2n+k+1}\\binom{2n+k+1}{2k}\\binom{2n-k+1}n$$ and $$\\binom{2k}k\\ \\bigg|\\ (2n+1)\\binom{2n}nC_{n+k}\\binom{n+k+1}{2k},$$ where $C_m$ denotes the Catalan number $\\frac1{m+1}\\binom{2m}m=\\binom{2m}m-\\binom{2m}{m+1}$. On the basis of these results, we obtain certain sums divisible by central binomial coefficients.<\/jats:p>","DOI":"10.37236\/3022","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T03:00:40Z","timestamp":1578711640000},"source":"Crossref","is-referenced-by-count":14,"title":["Products and Sums Divisible by Central Binomial Coefficients"],"prefix":"10.37236","volume":"20","author":[{"given":"Zhi-Wei","family":"Sun","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2013,1,18]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v20i1p9\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v20i1p9\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T22:20:27Z","timestamp":1579299627000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v20i1p9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,1,18]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2013,1,7]]}},"URL":"https:\/\/doi.org\/10.37236\/3022","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,1,18]]},"article-number":"P9"}}