a curious answer

*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 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,

**Follow-Ups**:**Re: a curious answer***From:*Devendra Kapadia <dkapadia@wolfram.com>

**Re: a curious answer***From:*"Chris Chiasson" <chris@chiasson.name>