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 A203244 #17 Feb 18 2025 03:54:49
%S A203244 4,84,1428,23188,372372,5963412,95436436,1527070356,24433475220,
%T A203244 390937001620,6254997618324,100079984262804,1601279837683348,
%U A203244 25620477760847508,409927645605215892,6558842335410077332,104941477389467729556
%N A203244 Second elementary symmetric function of the first n terms of (1,4,16,64,256,...).
%H A203244 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (21,-84,64).
%F A203244 a(n) = 4*A006105(n).
%F A203244 From _Colin Barker_, Aug 15 2014: (Start)
%F A203244 a(n) = (4-5*4^n+16^n)/45.
%F A203244 a(n) = 21*a(n-1)-84*a(n-2)+64*a(n-3).
%F A203244 G.f.: -4*x^2 / ((x-1)*(4*x-1)*(16*x-1)). (End)
%t A203244 f[k_] := 4^(k - 1); t[n_] := Table[f[k], {k, 1, n}]
%t A203244 a[n_] := SymmetricPolynomial[2, t[n]]
%t A203244 Table[a[n], {n, 2, 32}] (* A203244 *)
%t A203244 Table[a[n]/4, {n, 2, 32}] (* A006105 *)
%t A203244 LinearRecurrence[{21,-84,64},{4,84,1428},20] (* _Harvey P. Dale_, Aug 12 2015 *)
%o A203244 (PARI) Vec(-4*x^2/((x-1)*(4*x-1)*(16*x-1)) + O(x^100)) \\ _Colin Barker_, Aug 15 2014
%Y A203244 Cf. A006105.
%K A203244 nonn,easy
%O A203244 2,1
%A A203244 _Clark Kimberling_, Dec 31 2011
%E A203244 Typo in formula fixed by _Colin Barker_, Aug 15 2014