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 A204121 #10 Aug 02 2019 04:13:20
%S A204121 3,-1,14,-8,1,92,-68,15,-1,968,-816,230,-26,1,12096,-11248,3740,-564,
%T A204121 39,-1,199296,-198400,73544,-13192,1222,-56,1,3679488,-3877632,
%U A204121 1567824,-320304,36160,-2280,75,-1,82607616,-91008000
%N A204121 Array: row n shows the coefficients of the characteristic polynomial of the n-th principal submatrix of f(i,j) = gcd(prime(i+1), prime(j+1)) (A204120).
%C A204121 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 A204121 (For references regarding interlacing roots, see A202605.)
%e A204121 Top of the array:
%e A204121 3, -1;
%e A204121 14, -8, 1;
%e A204121 92, -68, 15, -1;
%e A204121 968, -816, 230, -26, 1;
%t A204121 f[i_, j_] := GCD[Prime[i + 1], Prime[j + 1]];
%t A204121 m[n_] := Table[f[i, j], {i, 1, n}, {j, 1, n}]
%t A204121 TableForm[m[8]] (* 8 X 8 principal submatrix *)
%t A204121 Flatten[Table[f[i, n + 1 - i],
%t A204121 {n, 1, 15}, {i, 1, n}]] (* A204120 *)
%t A204121 p[n_] := CharacteristicPolynomial[m[n], x];
%t A204121 c[n_] := CoefficientList[p[n], x]
%t A204121 TableForm[Flatten[Table[p[n], {n, 1, 10}]]]
%t A204121 Table[c[n], {n, 1, 12}]
%t A204121 Flatten[%] (* A204121 *)
%t A204121 TableForm[Table[c[n], {n, 1, 10}]]
%Y A204121 Cf. A204120, A202605, A204016.
%K A204121 tabl,sign
%O A204121 1,1
%A A204121 _Clark Kimberling_, Jan 11 2012