[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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