{"id":"W2404891737","doi":"","title":"Identities involving harmonic numbers and inverses of binomial coefficients.","year":2013,"lang":"en","type":"article","venue":"Ars Combinatoria","topic":"Advanced Mathematical Theories and Applications","field":"Physics and Astronomy","cited_by":0,"is_retracted":false,"has_abstract":false,"ca_institutions":"","funders":"","keywords":"Mathematics; Binomial coefficient; Harmonic number; Binomial (polynomial); Gaussian binomial coefficient; Central binomial coefficient; Harmonic; Pure mathematics; Applied mathematics; Negative binomial distribution; Statistics; Discrete mathematics; Poisson distribution","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":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.00003762491,0.00007332844,0.0001260502,0.00001902205,0.00007934937,0.000030448,0.00008347809,0.00001558084,0.000304477],"category_scores_gemma":[0.00000911379,0.00006856355,0.00003312746,0.00008306019,0.0001091942,0.0001409782,0.00007071996,0.00005213686,0.00004108439],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.000007302941,"about_ca_system_score_gemma":0.00001121329,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0001250119,"about_ca_topic_score_gemma":2.574714e-7,"domain_scores_codex":[0.9995543,0.000009731745,0.0001476038,0.0001024926,0.00006801942,0.0001178078],"domain_scores_gemma":[0.9996157,0.00008393241,0.00007055722,0.000130183,0.00005005551,0.00004954923],"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":[8.724448e-7,0.00005133144,0.002654098,0.00001288699,0.00001480674,3.708445e-8,0.0001454999,0.000002620873,0.0008537435,0.995102,0.0005995156,0.0005625222],"study_design_scores_gemma":[0.0002800694,0.00001340543,0.0003956752,0.00001433314,0.00001079351,1.439439e-7,0.0008780565,0.0001542479,0.003926989,0.9939249,0.0003243503,0.00007699324],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9925215,0.00003513318,0.0007963912,0.00004061438,0.0001424375,0.0001582585,0.000006769169,0.00001587958,0.006282985],"genre_scores_gemma":[0.9991754,0.000004528329,0.0004288225,0.00001287263,0.000007285695,0.00003748777,0.000004721555,0.000008215721,0.0003207157],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.006653819,"threshold_uncertainty_score":0.333381,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.009035073522629855,"score_gpt":0.2383999432038032,"score_spread":0.2293648696811734,"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."}}