[seqfan] Re: a number triangle I don't (yet) understand
israel at math.ubc.ca
israel at math.ubc.ca
Wed Jul 30 17:22:30 CEST 2014
The row sums are the values at z=1. Since phi(1)=1, the k=1 factor is 0
there. The first moment is the derivative evaluated at z=1. This is 0 for
n>1 because phi(1)=1 and phi(2)=1.
Cheers,
Robert Israel
On Jul 30 2014, Wouter Meeussen wrote:
>( 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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