Dan, the entry for the Bell numbers is A000110 there you will find: %F A000110 a(n) is asymptotic to n!*(2 Pi r^2 exp(r))^(-1/2) exp(exp(r)-1) / r^n, where r is the p\ ositive root of r exp(r) = n. - see e.g. the Odlyzko reference. Neil