%I #10 Jul 12 2012 00:39:54

%S 1,-1,1,-6,1,1,-12,20,-1,1,-27,165,-35,1,1,-123,1255,-511,54,-1,1,

%T -300,9266,-6003,1197,-82,1,1,-558,77523,-71564,20779,-2463,111,-1,1,

%U -2841,688624,-817771,315489,-54393,4386,-144,1,1,-9093

%N Array: row n shows the coefficients of the characteristic polynomial of the n-th principal submatrix of A203955.

%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...-6....1

%e 1...-12....20....-1

%e 1...-27....165...-35....1

%e 1...-123...1255..-511...54...-1

%t t = {1, 2, 3}; t1 = Flatten[{t, t, 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[%] (* A203956 *)

%t TableForm[Table[c[n], {n, 1, 10}]]

%Y Cf. A203955, A202605.

%K tabl,sign

%O 1,4

%A _Clark Kimberling_, Jan 08 2012