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A204161 Array: row n shows the coefficients of the characteristic polynomial of the n-th principal submatrix of (3i-2 if i=j and = 0 otherwise), as in A204160.

%I A204161 #6 Jul 12 2012 00:39:58
%S A204161 1,-1,3,-5,1,18,-36,12,-1,162,-360,153,-22,1,1944,-4644,2295,-435,35,
%T A204161 -1,29160,-73548,40419,-9135,990,-51,1,524880,-1382184,823284,-210924,
%U A204161 27720,-1953,70,-1,11022480
%N A204161 Array:  row n shows the coefficients of the characteristic polynomial of the n-th principal submatrix of (3i-2 if i=j and = 0 otherwise), as in A204160.
%C A204161 Let p(n)=p(n,x) be the characteristic polynomial of the n-th principal submatrix.  The zeros of p(n) are real, and they interlace the zeros of p(n+1).  See A202605 and A204016 for guides to related sequences.
%D A204161 (For references regarding interlacing roots, see A202605.)
%e A204161 Top of the array:
%e A204161 1.....-1
%e A204161 3.....-5.....1
%e A204161 18....-36....12....-1
%e A204161 162...-360...153...-22...1
%t A204161 f[i_, j_] := 1; f[i_, i_] := 2 i - 1;
%t A204161 m[n_] := Table[f[i, j], {i, 1, n}, {j, 1, n}]
%t A204161 TableForm[m[8]] (* 8x8 principal submatrix *)
%t A204161 Flatten[Table[f[i, n + 1 - i],
%t A204161   {n, 1, 15}, {i, 1, n}]]    (* A204160 *)
%t A204161 p[n_] := CharacteristicPolynomial[m[n], x];
%t A204161 c[n_] := CoefficientList[p[n], x]
%t A204161 TableForm[Flatten[Table[p[n], {n, 1, 10}]]]
%t A204161 Table[c[n], {n, 1, 12}]
%t A204161 Flatten[%]                   (* A204161 *)
%t A204161 TableForm[Table[c[n], {n, 1, 10}]]
%Y A204161 Cf. A204160, A202605, A204016.
%K A204161 tabl,sign
%O A204161 1,3
%A A204161 _Clark Kimberling_, Jan 12 2012