Re: a curious answer

*To*: mathgroup at smc.vnet.net*Subject*: [mg69127] Re: [mg69055] a curious answer*From*: "Chris Chiasson" <chris at chiasson.name>*Date*: Wed, 30 Aug 2006 06:35:08 -0400 (EDT)*References*: <200608290725.DAA28971@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

from the help: "CoefficientList[poly, var] gives a list of coefficients of powers of var in poly, starting with power 0." "Terms that do not contain positive integer powers of a particular variable are included in the first element of the list for that variable." Though I will say that CoefficientList[0,x] returning {} instead of {0} is appalling to me. On 8/29/06, rick <awass at umich.edu> 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, > > -- http://chris.chiasson.name/

**References**:**a curious answer***From:*"rick" <awass@umich.edu>