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A203954 Array: row n shows the coefficients of the characteristic polynomial of the n-th principal submatrix of A203953.

%I A203954 #10 Jul 12 2012 00:39:54
%S A203954 1,-1,1,-6,1,1,-20,12,-1,1,-70,75,-22,1,1,-264,406,-200,33,-1,1,-1034,
%T A203954 2085,-1470,430,-48,1,1,-4108,10296,-9600,4116,-816,64,-1,1,-16398,
%U A203954 49231,-57574,33135,-9786,1410,-84,1,1,-65552,229482
%N A203954 Array:  row n shows the coefficients of the characteristic polynomial of the n-th principal submatrix of A203953.
%C A203954 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 A203954 (For references regarding interlacing roots, see A202605.)
%e A203954 Top of the array:
%e A203954 1...-1
%e A203954 1...-6.....1
%e A203954 1...-20....12....-1
%e A203954 1...-70....75....-22....1
%e A203954 1...-264...406...-200...33...-1
%t A203954 t = {1, 2}; t1 = Flatten[{t, t, t, t, t, t, t, t, t, t}];
%t A203954 f[k_] := t1[[k]];
%t A203954 U[n_] :=
%t A203954   NestList[Most[Prepend[#, 0]] &, #, Length[#] - 1] &[
%t A203954    Table[f[k], {k, 1, n}]];
%t A203954 L[n_] := Transpose[U[n]];
%t A203954 p[n_] := CharacteristicPolynomial[L[n].U[n], x];
%t A203954 c[n_] := CoefficientList[p[n], x]
%t A203954 TableForm[Flatten[Table[p[n], {n, 1, 10}]]]
%t A203954 Table[c[n], {n, 1, 12}]
%t A203954 Flatten[%]  (* A203954 *)
%t A203954 TableForm[Table[c[n], {n, 1, 10}]]
%Y A203954 Cf. A203953, A202605.
%K A203954 tabl,sign
%O A203954 1,4
%A A203954 _Clark Kimberling_, Jan 08 2012