• To: mathgroup at smc.vnet.net
• Subject: [mg69055] a curious answer
• From: "rick" <awass at umich.edu>
• Date: Tue, 29 Aug 2006 03:25:34 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```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

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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