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%I #7 Jul 12 2012 00:39:54
%S 2,-1,7,-10,1,38,-71,28,-1,281,-610,357,-60,1,2634,-6329,4620,-1253,
%T 110,-1,29919,-77530,65613,-23348,3514,-182,1,399342,-1098271,1036044,
%U -442349,90800,-8442,280,-1,6125265
%N Array: row n shows the coefficients of the characteristic polynomial of the n-th principal submatrix of {(i+j)*min(i,j)} (A203990).
%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 for a guide to related sequences.
%D (For references regarding interlacing roots, see A202605.)
%e Top of the array:
%e 2.... -1
%e 7.... -10... 1
%e 38... -71... 28... -1
%e 281.. -610.. 357.. -60... 1
%t f[i_, j_] := (i + j) Min[i, j];
%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, 12}, {i, 1, n}]] (* A203990 *)
%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[%] (* A203991 *)
%t TableForm[Table[c[n], {n, 1, 10}]]
%Y Cf. A203990, A202605.
%K tabl,sign
%O 1,1
%A _Clark Kimberling_, Jan 09 2012
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