{"id":"W2157763597","doi":"10.4230/lipics.itp.2025.35","title":"An efficient algorithm for the computation of Bernoulli numbers","year":2007,"lang":"en","type":"preprint","venue":"ArXiv.org","topic":"Advanced Combinatorial Mathematics","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"Simon Fraser University","funders":"","keywords":"Bernoulli number; Computation; Mathematics; Product (mathematics); Combinatorics; Decimal; Function (biology); Bernoulli's principle; Euler's formula; Euler number (physics); Generating function; Prime (order theory); Asymptotic formula; Discrete mathematics; Algorithm; Arithmetic; Physics; Mathematical analysis; Backward Euler method; Geometry","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":[0.0009133831,0.0008424452,0.0009237063,0.001036684,0.001025165,0.001583283,0.001662239,0.0009075367,0.01217933],"category_scores_gemma":[0.003751808,0.0005429856,0.0007449492,0.001046399,0.001225673,0.002080585,0.002380991,0.001522203,0.005812766],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001742287,"about_ca_system_score_gemma":0.002082724,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001863746,"about_ca_topic_score_gemma":0.002655911,"domain_scores_codex":[0.9988632,0.0001734712,0.00007000907,0.0002371577,0.0003992711,0.00025694],"domain_scores_gemma":[0.9990543,0.0004027953,0.00006025713,0.0002442391,0.0001784,0.00006001053],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"design_other","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.00066263,0.0001273998,0.001739731,0.0005532281,0.00004607635,0.000384883,0.00055505,0.02318812,0.03724663,0.321059,0.03912739,0.57531],"study_design_scores_gemma":[0.0003681541,0.000203132,0.001097822,0.000228404,0.00005982108,0.0007446327,0.0001324265,0.2763763,0.06035762,0.528488,0.1317981,0.0001457309],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"genre_codex":"methods","genre_gemma":"methods","genre_scores_codex":[0.0101295,0.0002558472,0.9666571,0.0004407524,0.0001708825,0.0001479708,0.0002942481,0.01206906,0.009834671],"genre_scores_gemma":[0.1854857,0.000205332,0.7991297,0.0003370814,0.0001043646,0.0002849525,0.0009415504,0.001695927,0.01181532],"genre_candidate":"methods","genre_consensus":"methods","teacher_disagreement_score":0.01217933,"threshold_uncertainty_score":0.04074389,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.09510392372057169,"score_gpt":0.3913311536530508,"score_spread":0.2962272299324791,"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."}}