A002719

[Mitchell Harris]

On Fri, 30 Apr 2004, Emeric Deutsch wrote:

>There are only seven terms listed:
>1, 3, 16, 139, 1750, 29388, 623909,
>taken - I assume - from p. 147 of the cited Comtet paper.
>Same paper gives 
>G:=exp(-1+(exp(z)-1)/2)*sum(exp(s*(s-1)*z/2)/s!,s=0..infinity);
>as the exponential g.f. 
>Our computations (Maple and I) have given
>1, 3, 16, 139, 1750, 29388, 624889, 16255738, 504717929, 
>i.e. a discrepancy in the 7th term.
>
>Anybody interested in doublechecking?

confirmed w/ mathematica:

Ceiling[
  CoefficientList[
    Series[
      Exp[-1 + (Exp[z] - 1)/2]Sum[Exp[s(s - 1)z/2]/s!, {s, 0, 21}],
      {z, 0, 9}],
    z] 
  Table[n!, {n, 0, 9}]
]

gives:

{1, 1, 3, 16, 139, 1750, 29388, 624889, 16255738, 504717929}

-- 
Mitch Harris
Lehrstuhl fuer Automatentheorie, Fakultaet Informatik
Technische Universitaet Dresden, Deutschland
http://lat.inf.tu-dresden.de/~harris