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A203950 Array: row n shows the coefficients of the characteristic polynomial of the n-th principal submatrix of A203949.

%I A203950 #10 Jul 12 2012 00:39:54
%S A203950 1,-1,1,-3,1,1,-6,5,-1,1,-13,18,-8,1,1,-24,52,-40,12,-1,1,-39,131,
%T A203950 -155,78,-16,1,1,-58,291,-508,391,-138,21,-1,1,-81,584,-1410,1548,
%U A203950 -840,225,-27,1,1,-108,1078,-3448,5151,-4016,1658,-348,33,-1,1
%N A203950 Array:  row n shows the coefficients of the characteristic polynomial of the n-th principal submatrix of A203949.
%C A203950 Let p(n)=p(n,x) be the characteristic polynomial of the n-th principal submatrix.  The zeros of p(n) are positive, and they interlace the zeros of p(n+1).  See A202605 for a guide to related sequences.
%D A203950 (For references regarding interlacing roots, see A202605.)
%e A203950 Top of the array:
%e A203950 1...-1
%e A203950 1...-3....1
%e A203950 1...-6....5....-1
%e A203950 1...-13....18...-8....1
%e A203950 1...-24...52...-40...12...-1
%t A203950 t = {1, 1, 0}; t1 = Flatten[{t, t, t, t, t, t, t, t, t}];
%t A203950 f[k_] := t1[[k]];
%t A203950 U[n_] :=
%t A203950   NestList[Most[Prepend[#, 0]] &, #, Length[#] - 1] &[
%t A203950    Table[f[k], {k, 1, n}]];
%t A203950 L[n_] := Transpose[U[n]];
%t A203950 p[n_] := CharacteristicPolynomial[L[n].U[n], x];
%t A203950 c[n_] := CoefficientList[p[n], x]
%t A203950 TableForm[Flatten[Table[p[n], {n, 1, 10}]]]
%t A203950 Table[c[n], {n, 1, 12}]  (* A203950 *)
%t A203950 Flatten[%]
%t A203950 TableForm[Table[c[n], {n, 1, 10}]]
%Y A203950 Cf. A203949, A202605.
%K A203950 tabl,sign
%O A203950 1,4
%A A203950 _Clark Kimberling_, Jan 08 2012