       Re: a curious answer

• To: mathgroup at smc.vnet.net
• Subject: [mg69201] Re: a curious answer
• From: "rick" <awass at umich.edu>
• Date: Fri, 1 Sep 2006 18:40:58 -0400 (EDT)
• References: <ed0rfa\$skq\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Thank you for your response. One expects the occasional peculiar
behavior from a CAS ( and people too but that is another matter ;-)

rick wrote:
> Hi,
>
> Can anyone explain these answers (Out and Out)?
>
> Line 1 defines a polynomial in x that depends on n;
> line 2 tests the definition when n= 4;
> line 3 lists the coefficients of that polynomial and
> line 4 checks the list when n= 4; lines 5 and 6 ask for a closed form
> for the polynomial and coefficients (which is probably not possible). I
> expected no answer-not gibberish.
>
> In:=
> k[n_]:=Expand[Product[(j*x+n-j),{j,1,n-1}]]
>
> In:=
> k
>
> Out=
> \!\(6 + 26\ x + 26\ x\^2 + 6\ x\^3\)
>
> In:=
> cL[s_]:=CoefficientList[k[s],x]
>
>
> In:=
> cL
>
> Out=
> {6,26,26,6}
>
> In:=
> cL[n]
>
> Out=
> \!\({\(-\((\(-1\))\)\^n\)\ n\^\(\(-1\) + n\)\ \(\((\(-1\) + n)\)!\)}\)
>
> In:=
> k[n]
>
> Out=
> \!\(\(-\((\(-1\))\)\^n\)\ n\^\(\(-1\) + n\)\ \(\((\(-1\) + n)\)!\)\)
>
>
> Thanks,

```

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