[seqfan] a number triangle I don't (yet) understand

Wouter Meeussen wouter.meeussen at telenet.be
Wed Jul 30 12:58:24 CEST 2014


( ref: http://math.stackexchange.com/questions/801399)

prod(k=0..n; 1 - eulerphi(k) * z)  gives a polynome in z with coefficients

      1        
      1 -1       
      1 -2 1      
      1 -4 5 -2     
      1 -6 13 -12 4    
      1 -10 37 -64 52 -16   
      1 -12 57 -138 180 -120 32  
      1 -18 129 -480 1008 -1200 752 -192 


Why are all row sums for n>0 exactly zero?
Why are all the moments for n>1 zero?   
      1        
      1 -2       
      1 -4 3      
      1 -8 15 -8     
      1 -12 39 -48 20    
      1 -20 111 -256 260 -96   
      1 -24 171 -552 900 -720 224  
      1 -36 387 -1920 5040 -7200 5264 -1536 


How many number triangles have that property?
I remember having seen trangles with that property before.

I can’t shake the feeling of overlooking something obvious here,
so, if you see what it is, please tell me. I’m blushing preemptively here.

Wouter.



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