{"id":"W2076367270","doi":"10.1134/s1061920809040086","title":"Some identities and congruences involving a certain family of numbers","year":2009,"lang":"en","type":"article","venue":"Russian Journal of Mathematical Physics","topic":"Advanced Mathematical Identities","field":"Mathematics","cited_by":19,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Victoria","funders":"","keywords":"Congruence relation; Bernoulli number; Stirling numbers of the second kind; Mathematics; Stirling number; Stirling numbers of the first kind; Factorial; Euler's formula; Pure mathematics; Combinatorics; Mathematical analysis","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":[0.00263129,0.0004856581,0.0006693065,0.001631749,0.003501822,0.002652774,0.0006001931,0.00111702,0.003919845],"category_scores_gemma":[0.00703574,0.0003549395,0.001064749,0.001174714,0.00395028,0.00567995,0.001864473,0.002728734,0.0009893818],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001265903,"about_ca_system_score_gemma":0.001188596,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0009612513,"about_ca_topic_score_gemma":0.0004971713,"domain_scores_codex":[0.9979165,0.0004944674,0.0001746104,0.0004371564,0.0006892376,0.0002879789],"domain_scores_gemma":[0.9975055,0.0009428348,0.0003583594,0.000234349,0.0006785591,0.0002804387],"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":[0.0000126258,0.00001425543,0.0002854092,0.00002064371,0.000002681759,0.0002320232,0.0003236119,0.0001179864,0.0009174561,0.9947783,0.0003693315,0.002925705],"study_design_scores_gemma":[0.00001553095,0.00003987403,0.0005375004,0.00003193042,0.00001271396,0.0007869221,0.0002561062,0.002787933,0.001555104,0.9809203,0.01302911,0.00002686171],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.3317506,0.003778191,0.3997426,0.003101451,0.002381664,0.0001861517,0.0002829051,0.0002090283,0.2585674],"genre_scores_gemma":[0.8973608,0.002854928,0.07319634,0.0006662926,0.001700464,0.0001585301,0.0002932525,0.00009765545,0.02367167],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.003919845,"threshold_uncertainty_score":0.01391578,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03920171447362413,"score_gpt":0.3158032713090105,"score_spread":0.2766015568353863,"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."}}