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%I #10 Jul 12 2012 00:39:54
%S 1,-1,1,-2,1,1,-4,4,-1,1,-7,13,-7,1,1,-11,35,-31,10,-1,1,-16,74,-107,
%T 61,-14,1,1,-22,147,-308,275,-111,19,-1,1,-29,256,-763,1001,-629,186,
%U -24,1,1,-37,428,-1683,3013,-2721,1264,-291,30,-1,1,-46
%N Array: row n shows the coefficients of the characteristic polynomial of the n-th principal submatrix of A203947.
%C 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 (For references regarding interlacing roots, see A202605.)
%e Top of the array:
%e 1...-1
%e 1...-2....1
%e 1...-4....4....-1
%e 1...-7....13...-7....1
%e 1...-11...35...-31...10...-1
%t t = {1, 0, 1}; t1 = Flatten[{t, t, t, t, t, t, t}];
%t f[k_] := t1[[k]];
%t U[n_] :=
%t NestList[Most[Prepend[#, 0]] &, #, Length[#] - 1] &[
%t Table[f[k], {k, 1, n}]];
%t L[n_] := Transpose[U[n]];
%t p[n_] := CharacteristicPolynomial[L[n].U[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[%]
%t TableForm[Table[c[n], {n, 1, 10}]]
%Y Cf. A203947, A202605.
%K tabl,sign
%O 1,4
%A _Clark Kimberling_, Jan 08 2012
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