{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,15]],"date-time":"2026-01-15T02:31:18Z","timestamp":1768444278003,"version":"3.49.0"},"reference-count":59,"publisher":"Informa UK Limited","issue":"4","license":[{"start":{"date-parts":[[2021,10,26]],"date-time":"2021-10-26T00:00:00Z","timestamp":1635206400000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0\/"}],"content-domain":{"domain":["www.tandfonline.com"],"crossmark-restriction":true},"short-container-title":["Experimental Mathematics"],"published-print":{"date-parts":[[2023,10,2]]},"DOI":"10.1080\/10586458.2021.1982080","type":"journal-article","created":{"date-parts":[[2021,10,26]],"date-time":"2021-10-26T18:05:46Z","timestamp":1635271546000},"page":"641-656","update-policy":"https:\/\/doi.org\/10.1080\/tandf_crossmark_01","source":"Crossref","is-referenced-by-count":8,"title":["New Representations for all Sporadic Ap\u00e9ry-Like Sequences, With Applications to Congruences"],"prefix":"10.1080","volume":"32","author":[{"given":"Ofir","family":"Gorodetsky","sequence":"first","affiliation":[{"name":"Mathematical Institute, University of Oxford, Oxford, UK"}]}],"member":"301","published-online":{"date-parts":[[2021,10,26]]},"reference":[{"key":"e_1_3_4_2_1","first-page":"11","article-title":"Irrationalit\u00e9 de \u03b6(2) et","volume":"61","author":"Ap\u00e9ry R.","year":"1979","unstructured":"Ap\u00e9ry, R. (1979). Irrationalit\u00e9 de \u03b6(2) et \u03b6(3). Ast\u00e9risque, 61:11\u201313.","journal-title":"Ast\u00e9risque"},{"key":"e_1_3_4_3_1","first-page":"37","volume-title":"Mathematics, CTHS: Bull. Sec. Sci., III","author":"Ap\u00e9ry R.","year":"1981","unstructured":"Ap\u00e9ry, R. (1981). Interpolation de fractions continues et irrationalit\u00e9 de certaines constantes. In Mathematics, CTHS: Bull. Sec. Sci., III. Paris: Bib. Nat.; pp. 37\u201353."},{"issue":"3","key":"e_1_3_4_4_1","first-page":"255","article-title":"Supercongruences for the Almkvist-Zudilin numbers","volume":"173","author":"Amdeberhan T.","year":"2016","unstructured":"Amdeberhan, T., Tauraso, R. (2016). Supercongruences for the Almkvist-Zudilin numbers. Acta Arith. 173(3):255\u2013268.","journal-title":"Acta Arith"},{"key":"e_1_3_4_5_1","doi-asserted-by":"publisher","DOI":"10.1017\/S0013091509000959"},{"key":"e_1_3_4_6_1","first-page":"481","volume-title":"Mirror Symmetry. V, Vol. 38 of AMS\/IP Stud. Adv. Math","author":"Almkvist G.","year":"2006","unstructured":"Almkvist, G., Zudilin, W. (2006). Differential equations, mirror maps and zeta values. In Mirror Symmetry. V, Vol. 38 of AMS\/IP Stud. Adv. Math. Providence, RI: Amer. Math. Soc.; pp. 481\u2013515."},{"key":"e_1_3_4_7_1","doi-asserted-by":"publisher","DOI":"10.1088\/1751-8113\/46\/18\/185202"},{"key":"e_1_3_4_8_1","doi-asserted-by":"publisher","DOI":"10.1088\/1751-8113\/48\/50\/504001"},{"key":"e_1_3_4_9_1","first-page":"Art. B66a","article-title":"Explicit formula for the generating series of diagonal 3D rook paths","volume":"66","author":"Bostan A.","year":"2011","unstructured":"Bostan, A., Chyzak, F., van Hoeij, M., Pech, L. (2011\/12). Explicit formula for the generating series of diagonal 3D rook paths. S\u00e9m. Lothar. Combin. 66:Art. B66a, 27.","journal-title":"S\u00e9m. Lothar. Combin"},{"key":"e_1_3_4_10_1","doi-asserted-by":"publisher","DOI":"10.1016\/0022-314X(87)90025-4"},{"issue":"147","key":"e_1_3_4_11_1","first-page":"271","article-title":"Irrationality proofs using modular forms","author":"Beukers F.","year":"1987","unstructured":"Beukers, F. (1987). Irrationality proofs using modular forms. Ast\u00e9risque (147\/148):271\u2013283, 345. Journ\u00e9es arithm\u00e9tiques de Besan\u00e7on (Besan\u00e7on, 1985).","journal-title":"Ast\u00e9risque"},{"key":"e_1_3_4_12_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jsc.2016.04.002"},{"key":"e_1_3_4_13_1","doi-asserted-by":"publisher","DOI":"10.1007\/s11139-011-9325-y"},{"key":"e_1_3_4_14_1","first-page":"42","volume-title":"Den 11te Skandinaviske Matematikerkongress, Trondheim, 1949","author":"Viggo Brun J.","year":"1952","unstructured":"Viggo Brun, J., Stubban, O., Fjeldstad, J. E., Tambs Lyche, R., Aubert, K. E., Ljunggren, W., Jacobsthal, E. (1952). On the divisibility of the difference between two binomial coefficients. In Den 11te Skandinaviske Matematikerkongress, Trondheim, 1949. Johan Grundt Tanums Forlag, Oslo; pp. 42\u201354."},{"key":"e_1_3_4_15_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2016.01.017"},{"key":"e_1_3_4_16_1","doi-asserted-by":"publisher","DOI":"10.1080\/10586458.2013.748379"},{"key":"e_1_3_4_17_1","doi-asserted-by":"publisher","DOI":"10.1016\/0022-314X(80)90051-7"},{"key":"e_1_3_4_18_1","doi-asserted-by":"publisher","DOI":"10.1142\/S1793042110002879"},{"key":"e_1_3_4_19_1","volume-title":"Study group on ultrametric analysis, 10th year: 1982\/83, No. 2","author":"Christol G.","year":"1984","unstructured":"Christol, G. (1984). Diagonales de fractions rationnelles et equations diff\u00e9rentielles. In Amice, Y., Christol, G., Robba, P., eds. Study group on ultrametric analysis, 10th year: 1982\/83, No. 2, pages Exp. No. 18, 10. Paris: Inst. Henri Poincar\u00e9."},{"key":"e_1_3_4_20_1","volume-title":"Study group on ultrametric analysis, 12th year, 1984\/85, No. 1","author":"Christol G.","year":"1985","unstructured":"Christol, G. (1985). Diagonales de fractions rationnelles et \u00e9quations de Picard-Fuchs. In Amice, Y., Christol, G., Robba, P., eds. Study group on ultrametric analysis, 12th year, 1984\/85, No. 1, pages Exp. No. 13, 12. Paris: Secr\u00e9tariat Math."},{"key":"e_1_3_4_21_1","first-page":"115","volume-title":"Formal power series and algebraic combinatorics (Vienna)","author":"Chyzak F.","year":"1997","unstructured":"Chyzak, F. (1997). An extension of Zeilberger\u2019s fast algorithm to general holonomic functions. Vol. 217, pages 115\u2013134. 2000. Formal power series and algebraic combinatorics (Vienna)."},{"key":"e_1_3_4_22_1","doi-asserted-by":"publisher","DOI":"10.1007\/s11139-011-9357-3"},{"key":"e_1_3_4_23_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-56172-1"},{"key":"e_1_3_4_24_1","unstructured":"Coster M. J. (1988). Supercongruences . PhD thesis University of Leiden."},{"key":"e_1_3_4_25_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.aim.2011.06.011"},{"key":"e_1_3_4_26_1","doi-asserted-by":"publisher","DOI":"10.1112\/S0025579309000436"},{"key":"e_1_3_4_27_1","doi-asserted-by":"publisher","DOI":"10.1112\/S0010437X17007552"},{"key":"e_1_3_4_28_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jnt.2005.06.005"},{"key":"e_1_3_4_29_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF02684886"},{"key":"e_1_3_4_30_1","doi-asserted-by":"publisher","DOI":"10.1016\/0022-314X(82)90071-3"},{"key":"e_1_3_4_31_1","doi-asserted-by":"publisher","DOI":"10.1142\/S1793042119501069"},{"issue":"1","key":"e_1_3_4_32_1","first-page":"35","article-title":"On congruences in number-theory","volume":"10","author":"Kazandzidis G. S.","year":"1969","unstructured":"Kazandzidis, G. S. (1969). On congruences in number-theory. Bull. Soc. Math. Gr\u00e8ce (N.S.), 10(fasc., fasc. 1):35\u201340.","journal-title":"Bull. Soc. Math. Gr\u00e8ce (N.S.)"},{"key":"e_1_3_4_33_1","doi-asserted-by":"publisher","DOI":"10.1515\/crll.1852.44.93"},{"key":"e_1_3_4_34_1","doi-asserted-by":"publisher","DOI":"10.1016\/0021-8693(88)90166-4"},{"key":"e_1_3_4_35_1","first-page":"49","article-title":"Sur les congruences des nombres eul\u00e9riens et les coefficients diff\u00e9rentiels des functions trigonom\u00e9triques suivant un module premier","volume":"6","author":"Lucas E.","year":"1988","unstructured":"Lucas, E. (1988). Sur les congruences des nombres eul\u00e9riens et les coefficients diff\u00e9rentiels des functions trigonom\u00e9triques suivant un module premier. Bull. Soc. Math. Fr. 6:49\u201354.","journal-title":"Bull. Soc. Math. Fr"},{"key":"e_1_3_4_36_1","volume-title":"Combinatory analysis","author":"MacMahon P. A.","year":"1960","unstructured":"MacMahon, P. A. (1960). Combinatory analysis. Two volumes (bound as one). New York: Chelsea Publishing Co."},{"key":"e_1_3_4_37_1","doi-asserted-by":"publisher","DOI":"10.1080\/00029890.1992.11995840"},{"key":"e_1_3_4_38_1","doi-asserted-by":"publisher","DOI":"10.1016\/0022-314X(83)90038-0"},{"key":"e_1_3_4_39_1","doi-asserted-by":"publisher","DOI":"10.1142\/S1793042113500371"},{"key":"e_1_3_4_40_1","doi-asserted-by":"publisher","DOI":"10.1007\/s40993-016-0036-8"},{"key":"e_1_3_4_41_1","doi-asserted-by":"publisher","DOI":"10.1142\/S1793042116500184"},{"key":"e_1_3_4_42_1","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-2010-10771-2"},{"key":"e_1_3_4_43_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.aam.2011.03.002"},{"key":"e_1_3_4_44_1","doi-asserted-by":"publisher","DOI":"10.7169\/facm\/2013.48.1.3"},{"key":"e_1_3_4_45_1","doi-asserted-by":"publisher","DOI":"10.1017\/S0013091515000255"},{"key":"e_1_3_4_46_1","first-page":"110","volume-title":"Arithmetic of Complex Manifolds (Erlangen, 1988), Vol. 1399 of Lecture Notes in Math","author":"Peters C.","year":"1989","unstructured":"Peters, C., Stienstra, J. (1989). A pencil of K3-surfaces related to Ap\u00e9ry\u2019s recurrence for \u03b6(3) and Fermi surfaces for potential zero. In Barth, W. P., Lange, H., eds. Arithmetic of Complex Manifolds (Erlangen, 1988), Vol. 1399 of Lecture Notes in Math. Berlin: Springer; pp. 110\u2013127."},{"key":"e_1_3_4_47_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-3254-2"},{"key":"e_1_3_4_48_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF01455990"},{"key":"e_1_3_4_49_1","doi-asserted-by":"publisher","DOI":"10.1017\/S1446788700038350"},{"key":"e_1_3_4_50_1","unstructured":"Sloane N. J. A. (1996). The on-line encyclopedia of integer sequences. Available at: https:\/\/oeis.org."},{"key":"e_1_3_4_51_1","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(94)00118-3"},{"key":"e_1_3_4_52_1","doi-asserted-by":"publisher","DOI":"10.2140\/ant.2014.8.1985"},{"key":"e_1_3_4_53_1","doi-asserted-by":"publisher","DOI":"10.1007\/s40316-015-0031-9"},{"key":"e_1_3_4_54_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jat.2014.05.012"},{"key":"e_1_3_4_55_1","unstructured":"Verrill H. A. (1999). Some congruences related to modular forms. Max Planck Institute for Mathematics. Available at: http:\/\/www.mpim-bonn.mpg.de\/preprints?title=%22Some+congruences+related+to+modular+forms%22"},{"key":"e_1_3_4_56_1","doi-asserted-by":"publisher","DOI":"10.1090\/crmp\/030\/19"},{"key":"e_1_3_4_57_1","doi-asserted-by":"publisher","DOI":"10.1142\/S1793042110003587"},{"key":"e_1_3_4_58_1","doi-asserted-by":"publisher","DOI":"10.1090\/crmp\/047\/22"},{"key":"e_1_3_4_59_1","doi-asserted-by":"publisher","DOI":"10.4171\/176-1\/33"},{"key":"e_1_3_4_60_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0747-7171(08)80044-2"}],"container-title":["Experimental Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.tandfonline.com\/doi\/pdf\/10.1080\/10586458.2021.1982080","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,11,22]],"date-time":"2023-11-22T22:55:49Z","timestamp":1700693749000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.tandfonline.com\/doi\/full\/10.1080\/10586458.2021.1982080"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,10,26]]},"references-count":59,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2023,10,2]]}},"alternative-id":["10.1080\/10586458.2021.1982080"],"URL":"https:\/\/doi.org\/10.1080\/10586458.2021.1982080","relation":{},"ISSN":["1058-6458","1944-950X"],"issn-type":[{"value":"1058-6458","type":"print"},{"value":"1944-950X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,10,26]]},"assertion":[{"value":"The publishing and review policy for this title is described in its Aims & Scope.","order":1,"name":"peerreview_statement","label":"Peer Review Statement"},{"value":"http:\/\/www.tandfonline.com\/action\/journalInformation?show=aimsScope&journalCode=uexm20","URL":"http:\/\/www.tandfonline.com\/action\/journalInformation?show=aimsScope&journalCode=uexm20","order":2,"name":"aims_and_scope_url","label":"Aim & Scope"},{"value":"2021-10-26","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}