{"paper":{"title":"Sun's log-concavity conjecture on the Catalan-Larcombe-French sequence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"James J.Y. Zhao","submitted_at":"2015-05-25T14:43:03Z","abstract_excerpt":"Let $\\{P_n\\}_{n\\geq 0}$ denote the Catalan-Larcombe-French sequence, which naturally came up from the series expansion of the complete elliptic integral of the first kind. In this paper, we prove the strict log-concavity of the sequence $\\{\\sqrt[n]{P_n}\\}_{n\\geq 1}$, which was originally conjectured by Sun. We also obtain the strict log-concavity of the sequence $\\{\\sqrt[n]{V_n}\\}_{n\\geq 1}$, where $\\{V_n\\}_{n\\geq 0}$ is the Fennessey-Larcombe-French sequence arising in the series expansion of the complete elliptic integral of the second kind."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.06650","kind":"arxiv","version":2},"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"}