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 A269554 #31 Apr 28 2025 09:02:35
%S A269554 -1,-343,-33861,-3318283,-325158121,-31862177823,-3122168268781,
%T A269554 -305940628162963,-29979059391701841,-2937641879758617703,
%U A269554 -287858925156952833301,-28207237023501619046043,-2764021369378001713679161,-270845886962020666321511983,-26540132900908647297794495421
%N A269554 Expansion of (3*x^2 + 244*x + 1)/(x^3 - 99*x^2 + 99*x - 1).
%C A269554 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 q_k.
%H A269554 Seiichi Manyama, <a href="/A269554/b269554.txt">Table of n, a(n) for n = 0..500</a>
%H A269554 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 A269554 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (99,-99,1).
%F A269554 G.f.: (3*x^2 + 244*x + 1)/(x^3 - 99*x^2 + 99*x - 1).
%F A269554 a(n) = 31/12 + ((17*sqrt(6) - 43)/(2*sqrt(6) + 5)^(2*n) - (17*sqrt(6) + 43)*(2 sqrt(6) + 5)^(2*n))/24. - _Bruno Berselli_, Mar 02 2016
%t A269554 CoefficientList[Series[(3 x^2 + 244 x + 1)/(x^3 - 99 x^2 + 99 x - 1), {x, 0, 20}], x] (* or *) Table[Simplify[31/12 + ((17 Sqrt[6] - 43)/(2 Sqrt[6] + 5)^(2 n) - (17 Sqrt[6] + 43) (2 Sqrt[6] + 5)^(2 n))/24], {n, 0, 20}] (* _Bruno Berselli_, Mar 02 2016 *)
%t A269554 LinearRecurrence[{99,-99,1},{-1,-343,-33861},20] (* _Harvey P. Dale_, Feb 03 2025 *)
%o A269554 (PARI) Vec((3*x^2 + 244*x + 1)/(x^3 - 99*x^2 + 99*x - 1) + O(x^20))
%o A269554 (Sage)
%o A269554 gf = (3*x^2+244*x+1)/(x^3-99*x^2+99*x-1)
%o A269554 print(taylor(gf, x, 0, 20).list()) # _Bruno Berselli_, Mar 02 2016
%o A269554 (Magma) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!((3*x^2+244*x+1)/(x^3-99*x^2+99*x-1))); // _Bruno Berselli_, Mar 02 2016
%Y A269554 Cf. A010701, A261004, A269548, A269549, A269550, A269551, A269552, A269553, A269555, A269556.
%K A269554 sign,easy
%O A269554 0,2
%A A269554 _Michel Marcus_, Feb 29 2016