1,6

The row sums are all zero.

The idea of roots of polynomials of the sort came from the realization that in Umbral calculus for the expansion function:

p(x,t)=Sum(P(xd,n)*t^n/n!,{n,0,Infinity}];

to actually work there has to be a convergent limit:

Limit[P(x,n)*t^n/n!,n->Infinity]=0;

The idea that a point gets "trapped" in complex dynamics is the iterative:

Pc[x,n]=x

So if we look at polynomials as iterative steps, at a fixed point

the roots would be important dynamically.

Lennart Carleson, Theodore W. Gamelin, Complex Dynamics, Springer,New York,1993,Chapter II, page 27 ff

p(x,n)=T(x,n)-x:A053120[x,n]-x; out_n,m=Coefficients(A053120[x,n]-x).

{1, -1},

{0},

{-1, -1, 2},

{0, -4, 0, 4},

{1, -1, -8, 0, 8},

{0, 4, 0, -20, 0, 16},

{-1, -1,18, 0, -48, 0, 32},

{0, -8, 0, 56, 0, -112, 0, 64},

{1, -1, -32, 0, 160, 0, -256, 0, 128},

{0, 8, 0, -120, 0, 432, 0, -576, 0, 256},

{-1, -1,50, 0, -400, 0, 1120, 0, -1280, 0, 512}

Table[ChebyshevT[n, x] - x, {n, 0, 10}]; a = Table[CoefficientList[ChebyshevT[n, x] - x, x], {n, 0, 10}]; Flatten[{{1, -1}, {0}, {-1, -1, 2}, {0, -4, 0, 4}, {1, -1, -8, 0, 8}, {0, 4, 0, -20, 0, 16}, {-1, -1, 18, 0, -48, 0, 32}, {0, -8, 0, 56, 0, -112, 0, 64}, {1, -1, -32, 0, 160, 0, -256, 0, 128}, {0, 8, 0, -120, 0, 432, 0, -576, 0, 256}, {-1, -1, 50, 0, -400, 0, 1120, 0, -1280, 0, 512}}]

Sequence in context: A082519 A035688 A046769 this_sequence A082024 A114402 A035647

Adjacent sequences: A137558 A137559 A137560 this_sequence A137562 A137563 A137564

tabl,uned,sign

Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Apr 25 2008