{"id":"W2402339857","doi":"","title":"Identities of summations involving powers and inverse of binomial coefficients.","year":2011,"lang":"en","type":"article","venue":"Ars Combinatoria","topic":"Advanced Differential Equations and Dynamical Systems","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":false,"ca_institutions":"","funders":"","keywords":"Mathematics; Binomial coefficient; Inverse; Binomial (polynomial); Negative binomial distribution; Applied mathematics; Statistics; Combinatorics; Poisson distribution; Geometry","routes":{"ca_aff":false,"ca_fund":false,"ca_venue":true,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.002078274,0.0008305815,0.001007101,0.002938124,0.002368363,0.004188391,0.001220747,0.001025087,0.009373603],"category_scores_gemma":[0.00737321,0.0006450394,0.001190451,0.001714119,0.003388735,0.008476214,0.002520823,0.003400726,0.004349713],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001102919,"about_ca_system_score_gemma":0.0009288251,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0008154837,"about_ca_topic_score_gemma":0.00153723,"domain_scores_codex":[0.9983327,0.0004471324,0.000144314,0.0002485057,0.0006482914,0.0001791038],"domain_scores_gemma":[0.9978917,0.0008089553,0.0002269226,0.000309065,0.0005517694,0.0002116246],"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":[0.000004340013,0.000005915304,0.00004944923,0.00001844385,0.000003328625,0.00004414663,0.00009934289,0.00007740899,0.0002574373,0.9947744,0.00171482,0.002950995],"study_design_scores_gemma":[0.000004547007,0.000004739372,0.0001094569,0.00001951784,0.000006189854,0.0002207317,0.00003816178,0.001496832,0.000244769,0.9901512,0.007695131,0.000008794285],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"other","genre_gemma":"empirical","genre_scores_codex":[0.05953088,0.009607368,0.3904508,0.003200075,0.003371937,0.00007739802,0.0007049823,0.0004055896,0.532651],"genre_scores_gemma":[0.7137488,0.00735986,0.1244783,0.002116439,0.004353818,0.0002460809,0.0007864214,0.0006941379,0.1462161],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.009373603,"threshold_uncertainty_score":0.03135782,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04531914000292694,"score_gpt":0.27510397052995,"score_spread":0.2297848305270231,"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."}}