{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,1]],"date-time":"2026-01-01T03:14:22Z","timestamp":1767237262298,"version":"3.41.2"},"reference-count":9,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2006,3,5]],"date-time":"2006-03-05T00:00:00Z","timestamp":1141516800000},"content-version":"vor","delay-in-days":63,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"DOI":"10.13039\/501100008536","name":"Lanzhou University of Technology","doi-asserted-by":"crossref","id":[{"id":"10.13039\/501100008536","id-type":"DOI","asserted-by":"crossref"}]},{"name":"National Science Foundation of Gansu Province of China"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["International Journal of Mathematics and Mathematical Sciences"],"published-print":{"date-parts":[[2006,1]]},"abstract":"<jats:p>This paper presents a simple approach to invert the matrix <jats:italic>P<\/jats:italic><jats:sub><jats:italic>n<\/jats:italic><\/jats:sub> + <jats:italic>I<\/jats:italic><jats:sub><jats:italic>n<\/jats:italic><\/jats:sub> by applying the Euler polynomials and Bernoulli numbers,\nwhere <jats:italic>P<\/jats:italic><jats:sub><jats:italic>n<\/jats:italic><\/jats:sub> is the Pascal matrix.<\/jats:p>","DOI":"10.1155\/ijmms\/2006\/90901","type":"journal-article","created":{"date-parts":[[2006,4,2]],"date-time":"2006-04-02T14:23:36Z","timestamp":1143987816000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Explicit inverse of the Pascal matrix plus one"],"prefix":"10.1155","volume":"2006","author":[{"given":"Sheng-liang","family":"Yang","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhong-kui","family":"Liu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2006,3,5]]},"reference":[{"key":"e_1_2_1_1_2","doi-asserted-by":"publisher","DOI":"10.1080\/00029890.2001.11919745"},{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.1080\/00029890.2002.11920898"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0024-3795(99)00266-9"},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.1016\/0024\u20103795(92)90038\u2010C"},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.1080\/00029890.1993.11990415"},{"key":"e_1_2_1_6_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0893\u20109659(03)80058\u20107"},{"volume-title":"Advanced Combinatorics. The Art of Finite and Infinite Expansions","year":"1974","author":"Comtet L.","key":"e_1_2_1_7_2"},{"volume-title":"Handbook of Discrete and Combinatorial Mathematics","year":"2000","author":"Rosen K. H.","key":"e_1_2_1_8_2"},{"key":"e_1_2_1_9_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0893\u20109659(04)90077\u20108"}],"container-title":["International Journal of Mathematics and Mathematical Sciences"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/ijmms\/2006\/090901.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1155\/IJMMS\/2006\/90901","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,6,6]],"date-time":"2024-06-06T21:06:04Z","timestamp":1717707964000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1155\/IJMMS\/2006\/90901"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,1]]},"references-count":9,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2006,1]]}},"alternative-id":["10.1155\/IJMMS\/2006\/90901"],"URL":"https:\/\/doi.org\/10.1155\/ijmms\/2006\/90901","archive":["Portico"],"relation":{},"ISSN":["0161-1712","1687-0425"],"issn-type":[{"type":"print","value":"0161-1712"},{"type":"electronic","value":"1687-0425"}],"subject":[],"published":{"date-parts":[[2006,1]]},"assertion":[{"value":"2006-03-05","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"090901"}}