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<DIV>Seqfans - </DIV>
<DIV> Correction - since sequences
A080093 and A080094 are numerators </DIV>
<DIV>of coefficients, and to state the e.g.f.s so as to remove the powers
of 2 </DIV>
<DIV>in the denominators of the coefficients, I should have written:</DIV>
<DIV> </DIV>
<DIV>
<DIV>A080093 (after multiplying A080093(3*k+1) by 2, for k>=0),</DIV>
<DIV>{0,0,1,1,4,11,41,162,715,3425,17722,98253,...}:</DIV>
<DIV>E.g.f.: exp(exp(x) - 1 - x) - 1</DIV>
<DIV> </DIV>
<DIV>A080094 (after multiplying A080094(3*k+1) by 2, for k>=0),</DIV>
<DIV>{0,2,-3,3,-2,3,-5,-4,-5,55,212,201,...}:</DIV>
<DIV>E.g.f.: 1 - exp(1 - x - exp(x))</DIV>
<DIV> </DIV>
<DIV>instead of the statements below. </DIV>
<DIV> </DIV>
<DIV>Yet the formulas below are correct for evaluating Benoits'
sums,</DIV>
<DIV>which of course include the powers of 2 in the denominators.</DIV>
<DIV> </DIV>
<DIV>Paul</DIV></DIV>
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<DIV>A080093 (after multiplying A080093(3*k+1) by 2, for k>=0):
</DIV>
<DIV>E.g.f.: (exp(exp(x/2) - 1 - x/2) - 1)/2 </DIV>
<DIV> </DIV>
<DIV>A080094 (after multiplying A080094(3*k+1) by 2, for k>=0):</DIV>
<DIV>E.g.f.: (1 - exp(1 - x/2 -
exp(x/2)))/2</DIV></BLOCKQUOTE></BODY></HTML>