Generalized Bell Numbers - Correction

[Paul D. Hanna]

Seqfans - 
      Correction - since sequences A080093 and A080094 are numerators 
of coefficients, and to state the e.g.f.s so as to remove the powers of 2

in the denominators of the coefficients, I should have written:
 
A080093 (after multiplying A080093(3*k+1) by 2, for k>=0),
{0,0,1,1,4,11,41,162,715,3425,17722,98253,...}:
E.g.f.:  exp(exp(x) - 1 - x) - 1
 
A080094 (after multiplying A080094(3*k+1) by 2, for k>=0),
{0,2,-3,3,-2,3,-5,-4,-5,55,212,201,...}:
E.g.f.:  1 - exp(1 - x - exp(x))
 
instead of the statements below. 
 
Yet the formulas below are correct for evaluating Benoits' sums,
which of course include the powers of 2 in the denominators.
  
Paul
A080093 (after multiplying A080093(3*k+1) by 2, for k>=0):  
E.g.f.:  (exp(exp(x/2) - 1 - x/2) - 1)/2 

A080094 (after multiplying A080094(3*k+1) by 2, for k>=0):
E.g.f.:  (1 - exp(1 - x/2 - exp(x/2)))/2
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