Geodesic
The dual of Spivey's Bell number identity from Zeon algebra
Journal of integer sequences, Tome 20 (2017) no. 2
In this paper, we give a new short proof of the dual of Spivey's Bell number identity due to Mező. Our approach follows from basic manipulations involving a fundamental identity representing factorials in the Zeon algebra. This work, along with a previous one due to the author and dos Anjos, shows that Spivey's and Mező's identities have at their root a common underlying algebraic origin.
Classification : 11B73, 33B10, 05A15, 05A19
Keywords: zeon algebra, Berezin integration, Stirling number of the first kind, Pochhammer symbol, binomial coefficient, generating function 
@article{JIS_2017__20_2_a4,
     author = {Neto,  Ant\^onio Francisco},
     title = {The dual of {Spivey's} {Bell} number identity from {Zeon} algebra},
     journal = {Journal of integer sequences},
     year = {2017},
     volume = {20},
     number = {2},
     zbl = {1420.11051},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2017__20_2_a4/}
}
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Neto,  Antônio Francisco. The dual of Spivey's Bell number identity from Zeon algebra. Journal of integer sequences, Tome 20 (2017) no. 2. http://geodesic.mathdoc.fr/item/JIS_2017__20_2_a4/