{"paper":{"title":"Some binomial sums involving absolute values","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.ST","stat.TH"],"primary_cat":"math.CO","authors_text":"Helmut Prodinger, Hideyuki Ohtsuka, Judy-anne H. Osborn, Richard P. Brent","submitted_at":"2014-11-06T02:41:45Z","abstract_excerpt":"We consider several families of binomial sum identities whose definition involves the absolute value function. In particular, we consider centered double sums of the form \\[S_{\\alpha,\\beta}(n) := \\sum_{k,\\;\\ell}\\binom{2n}{n+k}\\binom{2n}{n+\\ell} |k^\\alpha-\\ell^\\alpha|^\\beta,\\] obtaining new results in the cases $\\alpha = 1, 2$. We show that there is a close connection between these double sums in the case $\\alpha=1$ and the single centered binomial sums considered by Tuenter."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.1477","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"}