{"title":"关于r-无序数的和","authors":"N. Ömür, K. Südemen, S. Koparal, Ö. Duran","doi":"10.46939/j.sci.arts-23.2-a14","DOIUrl":null,"url":null,"abstract":"In this paper, we derive some sums involving the r-derangement numbers, D_r (n) and the generalized hyperharmonic numbers of order r, H_n^r (α) by using the generating functions and Riordan arrays. For example, for n,r∈Z^+with n≥r,\n∑_(i=0)^(n-r)〖(-1)^i ((r+1i)) (D_r (n-i))/(n-i)!〗=(-1)^(n-r)/(n-r)!.","PeriodicalId":54169,"journal":{"name":"Journal of Science and Arts","volume":" ","pages":""},"PeriodicalIF":0.3000,"publicationDate":"2023-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"ON SUMS WITH THE r-DERANGEMENT NUMBERS\",\"authors\":\"N. Ömür, K. Südemen, S. Koparal, Ö. Duran\",\"doi\":\"10.46939/j.sci.arts-23.2-a14\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we derive some sums involving the r-derangement numbers, D_r (n) and the generalized hyperharmonic numbers of order r, H_n^r (α) by using the generating functions and Riordan arrays. For example, for n,r∈Z^+with n≥r,\\n∑_(i=0)^(n-r)〖(-1)^i ((r+1i)) (D_r (n-i))/(n-i)!〗=(-1)^(n-r)/(n-r)!.\",\"PeriodicalId\":54169,\"journal\":{\"name\":\"Journal of Science and Arts\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.3000,\"publicationDate\":\"2023-06-30\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Science and Arts\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.46939/j.sci.arts-23.2-a14\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MULTIDISCIPLINARY SCIENCES\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Science and Arts","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.46939/j.sci.arts-23.2-a14","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MULTIDISCIPLINARY SCIENCES","Score":null,"Total":0}
In this paper, we derive some sums involving the r-derangement numbers, D_r (n) and the generalized hyperharmonic numbers of order r, H_n^r (α) by using the generating functions and Riordan arrays. For example, for n,r∈Z^+with n≥r,
∑_(i=0)^(n-r)〖(-1)^i ((r+1i)) (D_r (n-i))/(n-i)!〗=(-1)^(n-r)/(n-r)!.
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