{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2026-05-26T00:16:20.000Z","description":"Problems submitted by members of the MATLAB Central community.","is_default":true,"created_by":161519,"badge_id":null,"featured":false,"trending":false,"solution_count_in_trending_period":0,"trending_last_calculated":"2026-05-26T00:00:00.000Z","image_id":null,"published":true,"community_created":false,"status_id":2,"is_default_group_for_player":false,"deleted_by":null,"deleted_at":null,"restored_by":null,"restored_at":null,"description_opc":null,"description_html":null,"published_at":null},"problems":[{"id":43754,"title":"Lah Numbers","description":"Create a square lower diagonal matrix containing the first n Lah number coefficients. In mathematics, the Lah numbers are coefficients expressing rising factorials in terms of falling factorials. For example, for n=8, the matrix of Lah numbers would be:\r\n\r\n  1\t0\t0\t0\t0\t0\t0\t0\t0\t0\t0\r\n2\t1\t0\t0\t0\t0\t0\t0\t0\t0\t0\r\n6\t6\t1\t0\t0\t0\t0\t0\t0\t0\t0\r\n24\t36\t12\t1\t0\t0\t0\t0\t0\t0\t0\r\n120\t240\t120\t20\t1\t0\t0\t0\t0\t0\t0\r\n720\t1800\t1200\t300\t30\t1\t0\t0\t0\t0\t0\r\n5040\t15120\t12600\t4200\t630\t42\t1\t0\t0\t0\t0\r\n40320\t141120\t141120\t58800\t11760\t1176\t56\t1\t0\t0\t0\r\n362880\t1451520\t1693440\t846720\t211680\t28224\t2016\t72\t1\t0\t0\r\n\r\nSee \u003chttps://en.wikipedia.org/wiki/Lah_number Lah Number\u003e for more information.","description_html":"\u003cp\u003eCreate a square lower diagonal matrix containing the first n Lah number coefficients. In mathematics, the Lah numbers are coefficients expressing rising factorials in terms of falling factorials. For example, for n=8, the matrix of Lah numbers would be:\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003e1\t0\t0\t0\t0\t0\t0\t0\t0\t0\t0\r\n2\t1\t0\t0\t0\t0\t0\t0\t0\t0\t0\r\n6\t6\t1\t0\t0\t0\t0\t0\t0\t0\t0\r\n24\t36\t12\t1\t0\t0\t0\t0\t0\t0\t0\r\n120\t240\t120\t20\t1\t0\t0\t0\t0\t0\t0\r\n720\t1800\t1200\t300\t30\t1\t0\t0\t0\t0\t0\r\n5040\t15120\t12600\t4200\t630\t42\t1\t0\t0\t0\t0\r\n40320\t141120\t141120\t58800\t11760\t1176\t56\t1\t0\t0\t0\r\n362880\t1451520\t1693440\t846720\t211680\t28224\t2016\t72\t1\t0\t0\r\n\u003c/pre\u003e\u003cp\u003eSee \u003ca href = \"https://en.wikipedia.org/wiki/Lah_number\"\u003eLah Number\u003c/a\u003e for more information.\u003c/p\u003e","function_template":"function y = lah(n)\r\n  y = x;\r\nend","test_suite":"%%\r\nx = 8;\r\ny_correct = [1,0,0,0,0,0,0,0,0;2,1,0,0,0,0,0,0,0;6,6,1,0,0,0,0,0,0;24,36,12,1,0,0,0,0,0;120,240,120,20,1,0,0,0,0;720,1800,1200,300,30,1,0,0,0;5040,15120,12600,4200,630,42,1,0,0;40320,141120,141120,58800,11760,1176,56,1,0;362880,1451520,1693440,846720,211680,28224,2016,72,1];\r\nassert(isequal(lah(x),y_correct))\r\n%%\r\nx = 1;\r\ny_correct = [1,0;2,1];\r\nassert(isequal(lah(x),y_correct))\r\n%%\r\nx = 3;\r\ny_correct = [1,0,0,0;2,1,0,0;6,6,1,0;24,36,12,1];\r\nassert(isequal(lah(x),y_correct))\r\n%%\r\nx = 10;\r\ny_correct = [1,0,0,0,0,0,0,0,0,0,0;2,1,0,0,0,0,0,0,0,0,0;6,6,1,0,0,0,0,0,0,0,0;24,36,12,1,0,0,0,0,0,0,0;120,240,120,20,1,0,0,0,0,0,0;720,1800,1200,300,30,1,0,0,0,0,0;5040,15120,12600,4200,630,42,1,0,0,0,0;40320,141120,141120,58800,11760,1176,56,1,0,0,0;362880,1451520,1693440,846720,211680,28224,2016,72,1,0,0;3628800,16329600,21772800,12700800,3810240,635040,60480,3240,90,1,0;39916800,199584000,299376000,199584000,69854400,13970880,1663200,118800,4950,110,1];\r\nassert(isequal(lah(x),y_correct))","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":93456,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":41,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2016-12-07T22:42:33.000Z","updated_at":"2026-05-14T03:05:31.000Z","published_at":"2016-12-07T22:42:33.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCreate a square lower diagonal matrix containing the first n Lah number coefficients. In mathematics, the Lah numbers are coefficients expressing rising factorials in terms of falling factorials. For example, for n=8, the matrix of Lah numbers would be:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[1  0  0  0  0  0  0  0  0  0  0\\n2  1  0  0  0  0  0  0  0  0  0\\n6  6  1  0  0  0  0  0  0  0  0\\n24  36  12  1  0  0  0  0  0  0  0\\n120  240  120  20  1  0  0  0  0  0  0\\n720  1800  1200  300  30  1  0  0  0  0  0\\n5040  15120  12600  4200  630  42  1  0  0  0  0\\n40320  141120  141120  58800  11760  1176  56  1  0  0  0\\n362880  1451520  1693440  846720  211680  28224  2016  72  1  0  0]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSee\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Lah_number\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eLah Number\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e for more information.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"}],"problem_search":{"problems":[{"id":43754,"title":"Lah Numbers","description":"Create a square lower diagonal matrix containing the first n Lah number coefficients. In mathematics, the Lah numbers are coefficients expressing rising factorials in terms of falling factorials. For example, for n=8, the matrix of Lah numbers would be:\r\n\r\n  1\t0\t0\t0\t0\t0\t0\t0\t0\t0\t0\r\n2\t1\t0\t0\t0\t0\t0\t0\t0\t0\t0\r\n6\t6\t1\t0\t0\t0\t0\t0\t0\t0\t0\r\n24\t36\t12\t1\t0\t0\t0\t0\t0\t0\t0\r\n120\t240\t120\t20\t1\t0\t0\t0\t0\t0\t0\r\n720\t1800\t1200\t300\t30\t1\t0\t0\t0\t0\t0\r\n5040\t15120\t12600\t4200\t630\t42\t1\t0\t0\t0\t0\r\n40320\t141120\t141120\t58800\t11760\t1176\t56\t1\t0\t0\t0\r\n362880\t1451520\t1693440\t846720\t211680\t28224\t2016\t72\t1\t0\t0\r\n\r\nSee \u003chttps://en.wikipedia.org/wiki/Lah_number Lah Number\u003e for more information.","description_html":"\u003cp\u003eCreate a square lower diagonal matrix containing the first n Lah number coefficients. In mathematics, the Lah numbers are coefficients expressing rising factorials in terms of falling factorials. For example, for n=8, the matrix of Lah numbers would be:\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003e1\t0\t0\t0\t0\t0\t0\t0\t0\t0\t0\r\n2\t1\t0\t0\t0\t0\t0\t0\t0\t0\t0\r\n6\t6\t1\t0\t0\t0\t0\t0\t0\t0\t0\r\n24\t36\t12\t1\t0\t0\t0\t0\t0\t0\t0\r\n120\t240\t120\t20\t1\t0\t0\t0\t0\t0\t0\r\n720\t1800\t1200\t300\t30\t1\t0\t0\t0\t0\t0\r\n5040\t15120\t12600\t4200\t630\t42\t1\t0\t0\t0\t0\r\n40320\t141120\t141120\t58800\t11760\t1176\t56\t1\t0\t0\t0\r\n362880\t1451520\t1693440\t846720\t211680\t28224\t2016\t72\t1\t0\t0\r\n\u003c/pre\u003e\u003cp\u003eSee \u003ca href = \"https://en.wikipedia.org/wiki/Lah_number\"\u003eLah Number\u003c/a\u003e for more information.\u003c/p\u003e","function_template":"function y = lah(n)\r\n  y = x;\r\nend","test_suite":"%%\r\nx = 8;\r\ny_correct = [1,0,0,0,0,0,0,0,0;2,1,0,0,0,0,0,0,0;6,6,1,0,0,0,0,0,0;24,36,12,1,0,0,0,0,0;120,240,120,20,1,0,0,0,0;720,1800,1200,300,30,1,0,0,0;5040,15120,12600,4200,630,42,1,0,0;40320,141120,141120,58800,11760,1176,56,1,0;362880,1451520,1693440,846720,211680,28224,2016,72,1];\r\nassert(isequal(lah(x),y_correct))\r\n%%\r\nx = 1;\r\ny_correct = [1,0;2,1];\r\nassert(isequal(lah(x),y_correct))\r\n%%\r\nx = 3;\r\ny_correct = [1,0,0,0;2,1,0,0;6,6,1,0;24,36,12,1];\r\nassert(isequal(lah(x),y_correct))\r\n%%\r\nx = 10;\r\ny_correct = [1,0,0,0,0,0,0,0,0,0,0;2,1,0,0,0,0,0,0,0,0,0;6,6,1,0,0,0,0,0,0,0,0;24,36,12,1,0,0,0,0,0,0,0;120,240,120,20,1,0,0,0,0,0,0;720,1800,1200,300,30,1,0,0,0,0,0;5040,15120,12600,4200,630,42,1,0,0,0,0;40320,141120,141120,58800,11760,1176,56,1,0,0,0;362880,1451520,1693440,846720,211680,28224,2016,72,1,0,0;3628800,16329600,21772800,12700800,3810240,635040,60480,3240,90,1,0;39916800,199584000,299376000,199584000,69854400,13970880,1663200,118800,4950,110,1];\r\nassert(isequal(lah(x),y_correct))","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":93456,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":41,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2016-12-07T22:42:33.000Z","updated_at":"2026-05-14T03:05:31.000Z","published_at":"2016-12-07T22:42:33.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCreate a square lower diagonal matrix containing the first n Lah number coefficients. In mathematics, the Lah numbers are coefficients expressing rising factorials in terms of falling factorials. For example, for n=8, the matrix of Lah numbers would be:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[1  0  0  0  0  0  0  0  0  0  0\\n2  1  0  0  0  0  0  0  0  0  0\\n6  6  1  0  0  0  0  0  0  0  0\\n24  36  12  1  0  0  0  0  0  0  0\\n120  240  120  20  1  0  0  0  0  0  0\\n720  1800  1200  300  30  1  0  0  0  0  0\\n5040  15120  12600  4200  630  42  1  0  0  0  0\\n40320  141120  141120  58800  11760  1176  56  1  0  0  0\\n362880  1451520  1693440  846720  211680  28224  2016  72  1  0  0]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSee\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Lah_number\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eLah Number\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e for more information.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"}],"errors":[],"facets":[[{"value":"Magic Numbers IV","count":1,"selected":false}],[{"value":"medium","count":1,"selected":false}]],"term":"tag:\"lah numbers\"","page":1,"per_page":50,"sort":"map(difficulty_value,0,0,999) asc"}}