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A203956 Array: row n shows the coefficients of the characteristic polynomial of the n-th principal submatrix of A203955.

%I A203956 #10 Jul 12 2012 00:39:54
%S A203956 1,-1,1,-6,1,1,-12,20,-1,1,-27,165,-35,1,1,-123,1255,-511,54,-1,1,
%T A203956 -300,9266,-6003,1197,-82,1,1,-558,77523,-71564,20779,-2463,111,-1,1,
%U A203956 -2841,688624,-817771,315489,-54393,4386,-144,1,1,-9093
%N A203956 Array:  row n shows the coefficients of the characteristic polynomial of the n-th principal submatrix of A203955.
%C A203956 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 A203956 (For references regarding interlacing roots, see A202605.)
%e A203956 Top of the array:
%e A203956 1...-1
%e A203956 1...-6....1
%e A203956 1...-12....20....-1
%e A203956 1...-27....165...-35....1
%e A203956 1...-123...1255..-511...54...-1
%t A203956 t = {1, 2, 3}; t1 = Flatten[{t, t, t, t, t, t, t, t, t}];
%t A203956 f[k_] := t1[[k]];
%t A203956 U[n_] :=
%t A203956   NestList[Most[Prepend[#, 0]] &, #, Length[#] - 1] &[
%t A203956    Table[f[k], {k, 1, n}]];
%t A203956 L[n_] := Transpose[U[n]];
%t A203956 p[n_] := CharacteristicPolynomial[L[n].U[n], x];
%t A203956 c[n_] := CoefficientList[p[n], x]
%t A203956 TableForm[Flatten[Table[p[n], {n, 1, 10}]]]
%t A203956 Table[c[n], {n, 1, 12}]
%t A203956 Flatten[%]  (* A203956 *)
%t A203956 TableForm[Table[c[n], {n, 1, 10}]]
%Y A203956 Cf. A203955, A202605.
%K A203956 tabl,sign
%O A203956 1,4
%A A203956 _Clark Kimberling_, Jan 08 2012