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 A296817 #18 Jan 27 2020 11:57:30
%S A296817 1,-9,56,-328,1912,-11144,64952,-378568,2206456,-12860168,74954552,
%T A296817 -436867144,2546248312,-14840622728,86497488056,-504144305608,
%U A296817 2938368345592,-17126065767944,99818026262072,-581782091804488,3390874524564856,-19763465055584648
%N A296817 Expansion of 1/Sum_{k>=0} (2*k+1)^2*x^k.
%H A296817 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (-6,-1).
%F A296817 a(n) = -6 * a(n-1) - a(n-2) for n > 3.
%F A296817 For n > 1, a(n) = 4*(-1)^n * ((sqrt(2)+1)^(2*n-1) - (sqrt(2)-1)^(2*n-1)). - _Vaclav Kotesovec_, Dec 21 2017
%F A296817 G.f.: (1-x)^3/(1+6*x+x^2). - _Robert Israel_, Dec 21 2017
%F A296817 a(n) = 8*A002315(n-1), n>1. - _R. J. Mathar_, Jan 27 2020
%p A296817 f:= gfun:-rectoproc({a(n) = -6 * a(n-1) - a(n-2), a(0)=1, a(1)=-9, a(2)=56, a(3)=-328},a(n),remember):
%p A296817 map(f, [$0..50]); # _Robert Israel_, Dec 21 2017
%t A296817 CoefficientList[Series[1/Sum[(2*k+1)^2*x^k, {k, 0, 30}], {x, 0, 30}], x] (* _Vaclav Kotesovec_, Dec 21 2017 *)
%t A296817 f[n_] := Simplify[ 4*(-1)^n*((Sqrt[2] +1)^(2n -1) - (Sqrt[2] -1)^(2n -1))]; f[0] = 1; f[1] = -9; Array[f, 22, 0] (* or *)
%t A296817 CoefficientList[ Series[-(x^3 -3x^2 +3x -1)/(x^2 +6x +1), {x, 0, 21}], x] (* or *)
%t A296817 Join[{1, -9}, LinearRecurrence[{-6, -1}, {56, -328}, 20]] (* _Robert G. Wilson v_, Dec 21 2017 *)
%o A296817 (PARI) N=66; x='x+O('x^N); Vec(1/sum(k=0, N, (2*k+1)^2*x^k))
%Y A296817 Cf. A016754, A115291.
%K A296817 sign,easy
%O A296817 0,2
%A A296817 _Seiichi Manyama_, Dec 21 2017