Explicit Expressions for Higher Order Binomial Convolutions of Numerical Sequences

  • José A. AdellEmail author
  • Alberto Lekuona


We give explicit expressions for higher order binomial convolutions of sequences of numbers having a finite exponential generating function. Illustrations involving Cauchy, Bernoulli, and Apostol–Euler numbers are presented. In these cases, we obtain formulas easy to compute in terms of Stirling numbers.


higher order convolutions exponential generating function Cauchy numbers Bernoulli numbers Apostol–Euler numbers Stirling numbers 

Mathematics Subject Classification

05A19 60E05 



We would like to thank the referee, whose comments and suggestions greatly improved the final outcome. The authors are partially supported by Research Projects DGA (E-64) and MTM2015-67006-P.


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Departamento de Métodos Estadísticos, Facultad de CienciasUniversidad de ZaragozaZaragozaSpain

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