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 A204119 #11 Aug 02 2019 04:13:16
%S A204119 2,-1,5,-5,1,22,-28,10,-1,140,-204,95,-17,1,1448,-2272,1210,-278,28,
%T A204119 -1,17856,-29680,17444,-4732,637,-41,1,291456,-504832,317576,-96040,
%U A204119 15386,-1328,58,-1,5338368,-9577728,6373968
%N A204119 Array: row n shows the coefficients of the characteristic polynomial of the n-th principal submatrix of f(i,j) = gcd(prime(i), prime(j)) (A204118).
%C A204119 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 A204119 (For references regarding interlacing roots, see A202605.)
%e A204119 Top of the array:
%e A204119 2, -1;
%e A204119 5, -5, 1;
%e A204119 22, -28, 10, -1;
%e A204119 140, -204, 95, -17, 1;
%t A204119 f[i_, j_] := GCD[Prime[i], Prime[j]];
%t A204119 m[n_] := Table[f[i, j], {i, 1, n}, {j, 1, n}]
%t A204119 TableForm[m[8]] (* 8 X 8 principal submatrix *)
%t A204119 Flatten[Table[f[i, n + 1 - i],
%t A204119 {n, 1, 15}, {i, 1, n}]] (* A204118 *)
%t A204119 p[n_] := CharacteristicPolynomial[m[n], x];
%t A204119 c[n_] := CoefficientList[p[n], x]
%t A204119 TableForm[Flatten[Table[p[n], {n, 1, 10}]]]
%t A204119 Table[c[n], {n, 1, 12}]
%t A204119 Flatten[%] (* A204119 *)
%t A204119 TableForm[Table[c[n], {n, 1, 10}]]
%Y A204119 Cf. A204118, A202605, A204016.
%K A204119 tabl,sign
%O A204119 1,1
%A A204119 _Clark Kimberling_, Jan 11 2012