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A204023 Array: row n shows the coefficients of the characteristic polynomial of the n-th principal submatrix of max(2i-1, 2j-1) (A204022).

%I A204023 #6 Jul 12 2012 00:39:58
%S A204023 1,-1,-6,-4,1,20,36,9,-1,-56,-160,-120,-16,1,144,560,700,300,25,-1,
%T A204023 -352,-1728,-3024,-2240,-630,-36,1,832,4928,11088,11760,5880,1176,49,
%U A204023 -1,-1920,-13312,-36608,-50688,-36960
%N A204023 Array:  row n shows the coefficients of the characteristic polynomial of the n-th principal submatrix of max(2i-1, 2j-1) (A204022).
%C A204023 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 A204023 (For references regarding interlacing roots, see A202605.)
%e A204023 Top of the array:
%e A204023  1....-1
%e A204023 -6....-4.....1
%e A204023  20....36....9.....-1
%e A204023 -56...-160..-120...-16....1
%t A204023 f[i_, j_] := Max[2 i - 1, 2 j - 1];
%t A204023 m[n_] := Table[f[i, j], {i, 1, n}, {j, 1, n}]
%t A204023 TableForm[m[6]] (* 6x6 principal submatrix *)
%t A204023 Flatten[Table[f[i, n + 1 - i],
%t A204023   {n, 1, 15}, {i, 1, n}]]  (* A204022 *)
%t A204023 p[n_] := CharacteristicPolynomial[m[n], x];
%t A204023 c[n_] := CoefficientList[p[n], x]
%t A204023 TableForm[Flatten[Table[p[n], {n, 1, 10}]]]
%t A204023 Table[c[n], {n, 1, 12}]
%t A204023 Flatten[%]                 (* A204023 *)
%t A204023 TableForm[Table[c[n], {n, 1, 10}]]
%Y A204023  Cf. A204022, A202605, A204016.
%K A204023 tabl,sign
%O A204023 1,3
%A A204023 _Clark Kimberling_, Jan 11 2012