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 A269556 #30 Apr 28 2025 09:02:25
%S A269556 5,347,33865,3318287,325158125,31862177827,3122168268785,
%T A269556 305940628162967,29979059391701845,2937641879758617707,
%U A269556 287858925156952833305,28207237023501619046047,2764021369378001713679165,270845886962020666321511987,26540132900908647297794495425,2600662178402085414517539039527
%N A269556 Expansion of (-7*x^2 + 148*x - 5)/(x^3 - 99*x^2 + 99*x - 1).
%C A269556 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 s_k.
%H A269556 Seiichi Manyama, <a href="/A269556/b269556.txt">Table of n, a(n) for n = 0..500</a>
%H A269556 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 A269556 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (99,-99,1).
%F A269556 G.f.: (-7*x^2 + 148*x - 5)/(x^3 - 99*x^2 + 99*x - 1).
%F A269556 a(n) = 17/12 + (-(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 A269556 CoefficientList[Series[(-7 x^2 + 148 x - 5)/(x^3 - 99 x^2 + 99 x - 1), {x, 0, 20}], x] (* or *) Table[Simplify[17/12 + (-(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 *)
%o A269556 (PARI) Vec((-7*x^2 + 148*x - 5)/(x^3 - 99*x^2 + 99*x - 1) + O(x^20))
%o A269556 (Sage)
%o A269556 gf = (-7*x^2+148*x-5)/(x^3-99*x^2+99*x-1)
%o A269556 print(taylor(gf, x, 0, 20).list()) # _Bruno Berselli_, Mar 02 2016
%o A269556 (Magma) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!((-7*x^2+148*x-5)/(x^3-99*x^2+99*x-1))); // _Bruno Berselli_, Mar 02 2016
%Y A269556 Cf. A010701, A261004, A269548, A269549, A269550, A269551, A269552, A269553, A269554, A269555.
%K A269556 nonn,easy
%O A269556 0,1
%A A269556 _Michel Marcus_, Feb 29 2016