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 A229463 #34 May 25 2025 09:22:36
%S A229463 1,28,731,19010,494265,12850896,334123303,8687205886,225867353045,
%T A229463 5872551179180,152686330658691,3969844597125978,103215959525275441,
%U A229463 2683614947657161480,69773988639086198495,1814123704616241160886,47167216320022270183053,1226347624320579024759396
%N A229463 Expansion of g.f. 1/((1-x)^2*(1-26*x)).
%C A229463 This sequence was chosen to illustrate a method of solution.
%H A229463 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (28,-53,26).
%F A229463 a(n) = (26^(n+2) - 25*n - 51)/625.
%F A229463 In general, for the expansion of 1/((1-s*x)^2*(1-r*x)) with r>s>=1 we have the formula: a(n) = (r^(n+2)- s^(n+1)*((r-s)*n +(2*r-s)))/(r-s)^2.
%F A229463 From _Elmo R. Oliveira_, May 24 2025: (Start)
%F A229463 E.g.f.: exp(x)*(-51 - 25*x + 676*exp(25*x))/625.
%F A229463 a(n) = 28*a(n-1) - 53*a(n-2) + 26*a(n-3). (End)
%e A229463 a(3) = (26^5 - 25*3 - 51)/625 = 19010.
%o A229463 (PARI) my(x='x+O('x^18)); Vec(1/((1-26*x)*(1-x)^2)) \\ _Elmo R. Oliveira_, May 24 2025
%Y A229463 Cf. A000295, A000340, A014825, A014827, A014936.
%K A229463 nonn,easy
%O A229463 0,2
%A A229463 _Yahia Kahloune_, Sep 24 2013