{"paper":{"title":"More properties of the Ramanujan sequence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Andrew Bakan, Luis Salinas, Stephan Ruscheweyh","submitted_at":"2016-05-18T08:34:21Z","abstract_excerpt":"The Ramanujan sequence $ \\{\\theta_{n}\\}_{n \\geq 0}$, defined as $$ \\theta_{0}= \\frac{1}{2} \\ , \\ \\ \\\n  \\theta_{n} = \\left(\\ \\ \\frac{e^{n}}{2} - \\sum_{k=0}^{n-1} \\frac{n^{k}}{k !} \\ \\\n  \\right) \\cdot \\frac{n !}{n^{n}} \\ , \\ \\ n \\geq 1 \\ ,$$ has been studied on many occasions and in many different contexts. J.Adell and P.Jodra (2008) and S. Koumandos (2013) showed, respectively, that the sequences $\\{\\theta_{n}\\}_{n \\geq 0}$ and $\\{4/135 - n \\cdot (\\theta_{n}- 1/3 )\\}_{n \\geq 0}$ are completely monotone. In the present paper we establish that the sequence $\\{(n+1)(\\theta_{n}- 1/3 )\\}_{n \\geq 0}$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.05479","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}