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%I #6 Jul 12 2012 00:39:58
%S 1,-1,2,-4,1,6,-16,10,-1,24,-76,70,-20,1,120,-428,496,-224,35,-1,720,
%T -2808,3808,-2260,588,-56,1,5040,-21096,32152,-23008,8140,-1344,84,-1,
%U 40320,-178848,298688,-245560,107328,-24772,2772
%N Array: row n shows the coefficients of the characteristic polynomial of the n-th principal submatrix of min(i(i+1)/2, j(j+1)/2) (A106255).
%C 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 (For references regarding interlacing roots, see A202605.)
%e Top of the array:
%e 1....-1
%e 2....-4....1
%e 6....-16...10...-1
%e 24...-76...70...-20....1
%t f[i_, j_] := Min[i (i + 1)/2, j (j + 1)/2];
%t m[n_] := Table[f[i, j], {i, 1, n}, {j, 1, n}]
%t TableForm[m[6]] (* 6x6 principal submatrix *)
%t Flatten[Table[f[i, n + 1 - i],
%t {n, 1, 15}, {i, 1, n}]] (* A106255 *)
%t p[n_] := CharacteristicPolynomial[m[n], x];
%t c[n_] := CoefficientList[p[n], x]
%t TableForm[Flatten[Table[p[n], {n, 1, 10}]]]
%t Table[c[n], {n, 1, 12}]
%t Flatten[%] (* A204024 *)
%t TableForm[Table[c[n], {n, 1, 10}]]
%Y Cf. A106255, A202605, A204016.
%K tabl,sign
%O 1,3
%A _Clark Kimberling_, Jan 11 2012
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