{"id":"W1969122989","doi":"10.1016/j.jnt.2010.05.005","title":"Asymptotics of a family of binomial sums","year":2010,"lang":"en","type":"article","venue":"Journal of Number Theory","topic":"Advanced Combinatorial Mathematics","field":"Mathematics","cited_by":5,"is_retracted":false,"has_abstract":false,"ca_institutions":"Dalhousie University","funders":"","keywords":"Mathematics; Binomial coefficient; Binomial (polynomial); Asymptotic expansion; Binomial theorem; Negative binomial distribution; Applied mathematics; Pure mathematics; Combinatorics; Mathematical analysis; Statistics; Poisson distribution","routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.004772665,0.001208265,0.001996984,0.007349005,0.00315626,0.005067431,0.00380276,0.003023508,0.01041618],"category_scores_gemma":[0.0435711,0.001260906,0.001505764,0.00253649,0.006346047,0.007166031,0.004098335,0.004205314,0.001249981],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00306112,"about_ca_system_score_gemma":0.001305558,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00116118,"about_ca_topic_score_gemma":0.0008506836,"domain_scores_codex":[0.9973254,0.0010077,0.0000980988,0.0003012356,0.0009343783,0.0003331272],"domain_scores_gemma":[0.9826424,0.01035024,0.001409937,0.0009473475,0.002324134,0.00232589],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.00004251571,0.00003782912,0.0007566083,0.0000691293,0.00001873102,0.0001412127,0.000155022,0.002924375,0.0006845681,0.9892161,0.001838586,0.004115333],"study_design_scores_gemma":[0.00003447994,0.00002407352,0.001041649,0.00008048518,0.00002606751,0.0007385267,0.00009774157,0.06420068,0.0003761873,0.9313253,0.00201272,0.00004208935],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.52913,0.006202891,0.263836,0.008325949,0.001540155,0.0001160004,0.0004058682,0.001296386,0.1891467],"genre_scores_gemma":[0.9453912,0.002405446,0.02439204,0.0008237755,0.002308511,0.0002608937,0.0005104461,0.0004705639,0.0234371],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.01041618,"threshold_uncertainty_score":0.03484559,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02957225183440293,"score_gpt":0.3363448887900402,"score_spread":0.3067726369556372,"validation_status":"score_only:v0-immature-baseline","note":"Baseline scores from an immature model (maturity gate not passed). Scores rank; they never assert a category."}}