Combinatorial Identities and Sums for Special Numbers and Polynomials

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FILOMAT, vol.32, no.20, pp.6869-6877, 2018 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 32 Issue: 20
  • Publication Date: 2018
  • Doi Number: 10.2298/fil1820869s
  • Journal Name: FILOMAT
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.6869-6877
  • Keywords: Euler numbers, Central factorial numbers, Array polynomials, Stirling numbers, Generating functions, Binomial coefficients, Combinatorial sum, EULER
  • Akdeniz University Affiliated: Yes


In this paper, by using some families of special numbers and polynomials with their generating functions and functional equations, we derive many new identities and relations related to these numbers and polynomials. These results are associated with well-known numbers and polynomials such as Euler numbers, Stirling numbers of the second kind, central factorial numbers and array polynomials. Furthermore, by using higher-order partial differential equations, we derive some combinatorial sums and identities. Finally, we give two computation algorithms for Euler numbers and central factorial numbers.