Geodesic
Implications of Spivey's Bell number formula
Journal of integer sequences, Tome 11 (2008) no. 3
Recently, Spivey discovered a novel formula for $B(n+m)$, where $B(n+m)$ is the $(n+m)^{th}$ Bell number. His proof was combinatorial in nature. This paper provides a generating function proof of Spivey's result. It also uses Spivey's formula to determine a new formula for $B(n)$. The paper concludes by extending all three identities to ordinary single variable Bell polynomials.
Classification : 11B73
Keywords: Bell number, Stirling number, Bell polynomial (Concerned with sequence ) 
@article{JIS_2008__11_3_a4,
     author = {Gould,  H.W. and Quaintance,  Jocelyn},
     title = {Implications of {Spivey's} {Bell} number formula},
     journal = {Journal of integer sequences},
     year = {2008},
     volume = {11},
     number = {3},
     zbl = {1204.11054},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2008__11_3_a4/}
}
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Gould,  H.W.; Quaintance,  Jocelyn. Implications of Spivey's Bell number formula. Journal of integer sequences, Tome 11 (2008) no. 3. http://geodesic.mathdoc.fr/item/JIS_2008__11_3_a4/