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 A269549 #31 Apr 28 2025 09:03:01
%S A269549 1,-199,-19799,-1940399,-190139599,-18631740599,-1825720439399,
%T A269549 -178901971320799,-17530567468999199,-1717816709990600999,
%U A269549 -168328507011609898999,-16494475870427779501199,-1616290306794910781218799,-158379955590030828779941399,-15519619357516226309653038599
%N A269549 Expansion of (-x^2 + 298*x - 1)/(x^3 - 99*x^2 + 99*x - 1).
%C A269549 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 c_k.
%H A269549 Seiichi Manyama, <a href="/A269549/b269549.txt">Table of n, a(n) for n = 0..500</a>
%H A269549 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 A269549 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (99,-99,1).
%F A269549 G.f.: (-x^2 + 298*x - 1)/(x^3 - 99*x^2 + 99*x - 1).
%F A269549 a(n) = 37/12 + ((2*sqrt(6) - 5)/(2*sqrt(6) + 5)^(2*n) - (2*sqrt(6) + 5)*(2*sqrt(6) + 5)^(2*n))*5/24. - _Bruno Berselli_, Mar 01 2016
%t A269549 CoefficientList[Series[(-x^2 + 298 x - 1)/(x^3 - 99 x^2 + 99 x - 1), {x, 0, 20}], x] (* or *) Table[FullSimplify[37/12 + ((2 Sqrt[6] - 5)/(2 Sqrt[6] + 5)^(2 n) - (2 Sqrt[6] + 5) (2 Sqrt[6] + 5)^(2 n)) 5/24], {n, 0, 20}] (* _Bruno Berselli_, Mar 01 2016 *)
%o A269549 (PARI) Vec((-x^2 + 298*x - 1)/(x^3 - 99*x^2 + 99*x - 1) + O(x^20))
%o A269549 (Sage)
%o A269549 gf = (-x^2+298*x-1)/(x^3-99*x^2+99*x-1)
%o A269549 print(taylor(gf, x, 0, 20).list()) # _Bruno Berselli_, Mar 01 2016
%o A269549 (Magma) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!((-x^2+298*x-1)/(x^3-99*x^2+99*x-1))); // _Bruno Berselli_, Mar 01 2016
%Y A269549 Cf. A010701, A261004, A269548, A269550, A269551, A269552, A269553, A269554, A269555, A269556.
%K A269549 sign,easy
%O A269549 0,2
%A A269549 _Michel Marcus_, Feb 29 2016