Geodesic
A generalized recurrence for Bell numbers
Journal of integer sequences, Tome 11 (2008) no. 2.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: We show that the two most well-known expressions for Bell numbers, $ \varpi_n = \sum_{k=0}^n \genfrac{\{}{\}}{0pt}{}{n}{k}$ and $ \varpi_{n+1} = \sum_{k=0}^n \binom{n}{k} \varpi_k$, are both special cases of a third expression for the Bell numbers, and we give a combinatorial proof of the latter.
Classification : 11B73
Keywords: Bell number, Stirling number 
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Spivey, Michael Z. A generalized recurrence for Bell numbers. Journal of integer sequences, Tome 11 (2008) no. 2. http://geodesic.mathdoc.fr/item/JIS_2008__11_2_a1/