A002719

[Meeussen Wouter (bkarnd)]

Ceiling[w=21 ;$MaxExtraPrecision=100;
  CoefficientList[
    Series[
      Exp[-1 + (Exp[z] - 1)/2]Sum[Exp[s(s - 1)z/2]/s!, {s, 0, 3w}],
      {z, 0, w}],
    z] 
  Table[n!, {n, 0, w}]
]

gives 
{1, 1, 3, 16, 139, 1750, 29388, 624889, 16255738, 504717929, 18353177160,
769917601384, 36803030137203, 1984024379014193, 119571835094300406,
7995677265437541258, 589356399302126773920, 47609742627231823142029,
4193665147256300117666879, 400955337829516224119020233,
41440870423841872676870218747, 4613078815253638377178567045525}

W.

> -----Original Message-----
> From: Mitchell Harris [mailto:harris at tcs.inf.tu-dresden.de]
> Sent: vrijdag 30 april 2004 15:40
> To: Emeric Deutsch
> Cc: seqfan at ext.jussieu.fr
> Subject: Re: A002719
> 
> 
> 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
> 
> 


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