... but if you happen to know an asymptotic formula I'd love if you'd post it.
The EIS entry for the Bell numbers has two: a(n) is asymptotic to n!*(2 Pi r^2 exp(r))^(-1/2) exp(exp(r)-1) / r^n, where r is the positive root of r exp(r) = n. - see e.g. the Odlyzko reference. a(n) is asymptotic to b^n*exp(b-n-1/2)/sqrt(ln(n)) where b satisfies b*ln(b) = n - 1/2 (see Graham, Knuth and Patashnik, Concrete Mathematics, 2nd ed., p. 493) - Benoit Cloitre (abmt(AT)wanadoo.fr), Oct 23 2002 --Michael
I wrote about 10 days ago: << Suppose you want to count all possible partitions of the set X_n = {1,2,...,n}. I.e., you want to know how many [collections of mutually disjoint nonempty subsets of X_n] have union = X_n. . . .
Michael Kleber wrote: << These are the Bell numbers, B(n). A000110 in the EIS, where you can find formulas and references to your heart's content.
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