Journal of Integer Sequences, Vol. 18 (2015), Article 15.5.6

Carlitz’s Identity for the Bernoulli Numbers and Zeon Algebra

Antônio Francisco Neto
DEPRO, Escola de Minas
Campus Morro do Cruzeiro, UFOP
35400-000 Ouro Preto MG


In this work we provide a new short proof of Carlitz's identity for the Bernoulli numbers. Our approach is based on the ordinary generating function for the Bernoulli numbers and a Grassmann-Berezin integral representation of the Bernoulli numbers in the context of the Zeon algebra, which comprises an associative and commutative algebra with nilpotent generators.

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(Concerned with sequences A027641 A027642.)

Received January 29 2015; revised version received April 6 2015. Published in Journal of Integer Sequences, May 25 2015.

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