Asymptotic Limit and Bounds
Several asymptotic formulae for the Bell numbers are known. One such is
Here
where W is the Lambert W function. (Lovász, 1993)
Moser and Wyman established the expansion
uniformly for as, where and each and are known expressions in .
In (Berend, D. and Tassa, T., 2010), the following bounds were established:
moreover, if then for all ,
where and 
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