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 A269551 #34 Apr 28 2025 09:02:50
%S A269551 5,237,22965,2250077,220484325,21605213517,2117090440085,
%T A269551 207453257914557,20328302185186245,1991966160890337197,
%U A269551 195192355465067858805,19126858869415759825437,1874236976847279395033765,183656096872163964953483277,17996423256495221286046327125,1763465823039659522067586574717
%N A269551 Expansion of (3*x^2 + 258*x - 5)/(x^3 - 99*x^2 + 99*x - 1).
%C A269551 Mc Laughlin (2010) gives an identity relating ten sequences, denoted a_k, b_k, ..., f_k, p_k, q_k, r_k, s_k. This is the sequence e_k.
%H A269551 Seiichi Manyama, <a href="/A269551/b269551.txt">Table of n, a(n) for n = 0..500</a>
%H A269551 J. Mc Laughlin, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Papers1/48-1/McLaughlin.pdf">An identity motivated by an amazing identity of Ramanujan</a>, Fib. Q., 48 (No. 1, 2010), 34-38.
%H A269551 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (99,-99,1).
%F A269551 G.f.: (3*x^2 + 258*x - 5)/(x^3 - 99*x^2 + 99*x - 1).
%F A269551 a(n) = 8/3 + (-(3*sqrt(6) - 7)/(2*sqrt(6) + 5)^(2*n) + (3*sqrt(6) + 7)*(2*sqrt(6) + 5)^(2*n))/6. - _Bruno Berselli_, Mar 01 2016
%t A269551 CoefficientList[Series[(3 x^2 + 258 x - 5)/(x^3 - 99 x^2 + 99 x - 1), {x, 0, 20}], x] (* or *) Table[FullSimplify[8/3 + (-(3 Sqrt[6] - 7)/(2 Sqrt[6] + 5)^(2 n) + (3 Sqrt[6] + 7) (2 Sqrt[6] + 5)^(2 n))/6], {n, 0, 20}] (* _Bruno Berselli_, Mar 01 2016 *)
%o A269551 (PARI) Vec((3*x^2 + 258*x - 5)/(x^3 - 99*x^2 + 99*x - 1) + O(x^20))
%o A269551 (Sage)
%o A269551 gf = (3*x^2+258*x-5)/(x^3-99*x^2+99*x-1)
%o A269551 print(taylor(gf, x, 0, 20).list()) # _Bruno Berselli_, Mar 01 2016
%o A269551 (Magma) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!((3*x^2+258*x-5)/(x^3-99*x^2+99*x-1))); // _Bruno Berselli_, Mar 01 2016
%Y A269551 Cf. A010701, A261004, A269548, A269549, A269550, A269552, A269553, A269554, A269555, A269556.
%K A269551 nonn,easy
%O A269551 0,1
%A A269551 _Michel Marcus_, Feb 29 2016