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 A204025 #9 Aug 02 2019 04:12:08
%S A204025 1,-1,1,-3,1,2,-8,6,-1,4,-20,26,-10,1,16,-88,134,-72,15,-1,32,-240,
%T A204025 496,-408,143,-21,1,192,-1504,3352,-3112,1344,-284,28,-1,768,-6400,
%U A204025 16320,-18496,10508,-3108,480,-36,1,4608,-39936,109952
%N A204025 Array: row n shows the coefficients of the characteristic polynomial of the n-th principal submatrix of gcd(i,j) (A003989).
%C A204025 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 A204025 (For references regarding interlacing roots, see A202605.)
%e A204025 Top of the array:
%e A204025 1, -1;
%e A204025 1, -3, 1;
%e A204025 2, -8, 6, -1;
%e A204025 4, -20, 26, -10, 1;
%t A204025 f[i_, j_] := GCD[i, j]
%t A204025 m[n_] := Table[f[i, j], {i, 1, n}, {j, 1, n}]
%t A204025 TableForm[m[6]] (* 6 X 6 principal submatrix *)
%t A204025 Flatten[Table[f[i, n + 1 - i],
%t A204025 {n, 1, 15}, {i, 1, n}]] (* A003989 *)
%t A204025 p[n_] := CharacteristicPolynomial[m[n], x];
%t A204025 c[n_] := CoefficientList[p[n], x]
%t A204025 TableForm[Flatten[Table[p[n], {n, 1, 10}]]]
%t A204025 Table[c[n], {n, 1, 12}]
%t A204025 Flatten[%] (* A204025 *)
%t A204025 TableForm[Table[c[n], {n, 1, 10}]]
%Y A204025 Cf. A003989, A202605, A204016.
%K A204025 tabl,sign
%O A204025 1,4
%A A204025 _Clark Kimberling_, Jan 11 2012