{"id":"W2084360633","doi":"10.1016/j.jmaa.2012.08.004","title":"On a sequence of sparse binomial-type polynomials","year":2012,"lang":"en","type":"article","venue":"Journal of Mathematical Analysis and Applications","topic":"Advanced Mathematical Identities","field":"Mathematics","cited_by":4,"is_retracted":false,"has_abstract":false,"ca_institutions":"Dalhousie University","funders":"","keywords":"Mathematics; Sequence (biology); Type (biology); Algebraic number; Binomial coefficient; Difference polynomials; Combinatorics; Distribution (mathematics); Pure mathematics; Orthogonal polynomials; Discrete mathematics; Algebra over a field; 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":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0009135676,0.0001499852,0.0007867279,0.0003213783,0.00006409646,0.00002433633,0.0002023645,0.00006882865,0.000317066],"category_scores_gemma":[0.0009803262,0.0001057081,0.0002978881,0.0006710815,0.000171083,0.0001898929,0.0000516658,0.0001549966,0.00002834748],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00003219635,"about_ca_system_score_gemma":0.00002687431,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000001205223,"about_ca_topic_score_gemma":8.708543e-7,"domain_scores_codex":[0.9981886,0.00005550835,0.001068271,0.0001058892,0.0003756465,0.0002061554],"domain_scores_gemma":[0.9966272,0.001758154,0.0008354701,0.0003310312,0.0002416469,0.0002065337],"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":[0.00001988184,0.0007716974,0.0002380878,0.0002189461,0.0005933521,8.700488e-7,0.0003124256,0.00002244241,0.003968733,0.9930699,0.0003129982,0.0004706649],"study_design_scores_gemma":[0.0001844036,0.00007644508,0.0001525245,0.00008033017,0.00175959,0.00003364044,0.0002613261,0.0002361261,0.003879887,0.9929526,0.0002594047,0.000123765],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.5563967,0.0003703973,0.4376153,0.0003851623,0.00004253775,0.0004007041,0.00002619352,0.00002667196,0.004736348],"genre_scores_gemma":[0.935881,0.00007525329,0.06335197,0.00003053739,0.0001366822,0.00001694466,0.000001256432,0.00001631938,0.0004899995],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.3794843,"threshold_uncertainty_score":0.431065,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.0779584640305621,"score_gpt":0.3673964769138064,"score_spread":0.2894380128832443,"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."}}