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MathGroup Archive 2006

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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[5] and Out[6])?
>
> 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[1]:=
> k[n_]:=Expand[Product[(j*x+n-j),{j,1,n-1}]]
>
> In[2]:=
> k[4]
>
> Out[2]=
> \!\(6 + 26\ x + 26\ x\^2 + 6\ x\^3\)
>
> In[3]:=
> cL[s_]:=CoefficientList[k[s],x]
>
>
> In[4]:=
> cL[4]
>
> Out[4]=
> {6,26,26,6}
>
> In[5]:=
> cL[n]
>
> Out[5]=
> \!\({\(-\((\(-1\))\)\^n\)\ n\^\(\(-1\) + n\)\ \(\((\(-1\) + n)\)!\)}\)
>
> In[6]:=
> k[n]
>
> Out[6]=
> \!\(\(-\((\(-1\))\)\^n\)\ n\^\(\(-1\) + n\)\ \(\((\(-1\) + n)\)!\)\)
> 
> 
> Thanks,


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