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 A204117 #10 Aug 02 2019 04:12:31
%S A204117 1,-1,2,-4,1,12,-28,11,-1,144,-360,182,-26,1,4320,-11088,5940,-984,57,
%T A204117 -1,233280,-616032,348768,-64728,4506,-120,1,29393280,-78086592,
%U A204117 44775936,-8554608,636444,-19740,247,-1,7054387200
%N A204117 Array: row n shows the coefficients of the characteristic polynomial of the n-th principal submatrix of f(i,j) = gcd(2^i-1, 2^j-1) (A204116).
%C A204117 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 A204117 (For references regarding interlacing roots, see A202605.)
%e A204117 Top of the array:
%e A204117 1, -1;
%e A204117 2, -4, 1;
%e A204117 12, -28, 11, -1;
%e A204117 144, -360, 182, -26, 1;
%t A204117 f[i_, j_] := GCD[2^i - 1, 2^j - 1];
%t A204117 m[n_] := Table[f[i, j], {i, 1, n}, {j, 1, n}]
%t A204117 TableForm[m[8]] (* 8 X 8 principal submatrix *)
%t A204117 Flatten[Table[f[i, n + 1 - i],
%t A204117 {n, 1, 15}, {i, 1, n}]] (* A204116 *)
%t A204117 p[n_] := CharacteristicPolynomial[m[n], x];
%t A204117 c[n_] := CoefficientList[p[n], x]
%t A204117 TableForm[Flatten[Table[p[n], {n, 1, 10}]]]
%t A204117 Table[c[n], {n, 1, 12}]
%t A204117 Flatten[%] (* A204117 *)
%t A204117 TableForm[Table[c[n], {n, 1, 10}]]
%Y A204117 Cf. A204116, A202605, A204016.
%K A204117 tabl,sign
%O A204117 1,3
%A A204117 _Clark Kimberling_, Jan 11 2012