This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A204169 #7 Jul 12 2012 00:39:59
%S A204169 1,-1,-1,-4,1,0,6,9,-1,0,0,-20,-16,1,0,0,0,50,25,-1,0,0,0,0,-105,-36,
%T A204169 1,0,0,0,0,0,196,49,-1,0,0,0,0,0,0,-336,-64,1,0,0,0,0,0,0,0,540,81,-1,
%U A204169 0,0,0,0,0,0,0,0,-825,-100,1
%N A204169 Array: row n shows the coefficients of the characteristic polynomial of the n-th principal submatrix of (i+j-1), as in A002024.
%C A204169 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 A204169 (For references regarding interlacing roots, see A202605.)
%e A204169 Top of the array:
%e A204169 2....-1
%e A204169 -1....-4.....1
%e A204169 0.....6.....9....-1
%e A204169 0.....0....-20...-16...1
%t A204169 f[i_, j_] := i + j - 1;
%t A204169 m[n_] := Table[f[i, j], {i, 1, n}, {j, 1, n}]
%t A204169 TableForm[m[8]] (* 8x8 principal submatrix *)
%t A204169 Flatten[Table[f[i, n + 1 - i],
%t A204169 {n, 1, 15}, {i, 1, n}]] (* A002024 *)
%t A204169 p[n_] := CharacteristicPolynomial[m[n], x];
%t A204169 c[n_] := CoefficientList[p[n], x]
%t A204169 TableForm[Flatten[Table[p[n], {n, 1, 10}]]]
%t A204169 Table[c[n], {n, 1, 12}]
%t A204169 Flatten[%] (* A204169 *)
%t A204169 TableForm[Table[c[n], {n, 1, 10}]]
%Y A204169 Cf. A002024, A202605, A204016.
%K A204169 tabl,sign
%O A204169 1,4
%A A204169 _Clark Kimberling_, Jan 12 2012