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 A269548 Expansion of (-7*x^2 + 134*x + 1)/(x^3 - 99*x^2 + 99*x - 1). 8
 -1, -233, -22961, -2250073, -220484321, -21605213513, -2117090440081, -207453257914553, -20328302185186241, -1991966160890337193, -195192355465067858801, -19126858869415759825433, -1874236976847279395033761, -183656096872163964953483273, -17996423256495221286046327121 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS 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 b_k. LINKS Table of n, a(n) for n=0..14. J. Mc Laughlin, An identity motivated by an amazing identity of Ramanujan, Fib. Q., 48 (No. 1, 2010), 34-38. Index entries for linear recurrences with constant coefficients, signature (99,-99,1). FORMULA G.f.: (-7*x^2 + 134*x + 1)/(x^3 - 99*x^2 + 99*x - 1). a(n) = 4/3 + ((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 MATHEMATICA CoefficientList[Series[(-7 x^2 + 134 x + 1)/(x^3 - 99 x^2 + 99 x - 1), {x, 0, 20}], x] (* or *) Table[FullSimplify[4/3 + ((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 *) PROG (PARI) Vec((-7*x^2 + 134*x + 1)/(x^3 - 99*x^2 + 99*x - 1) + O(x^20)) (Sage) gf = (-7*x^2+134*x+1)/(x^3-99*x^2+99*x-1) print(taylor(gf, x, 0, 20).list()) # Bruno Berselli, Mar 01 2016 (Magma) m:=20; R:=PowerSeriesRing(Integers(), m); Coefficients(R!((-7*x^2+134*x+1)/(x^3-99*x^2+99*x-1))); // Bruno Berselli, Mar 01 2016 CROSSREFS Cf. A261004, A269549, A269550, A269551, A269552, A269553, A269554, A269555, A269556. Sequence in context: A201214 A232322 A264069 * A264021 A256086 A186897 Adjacent sequences: A269545 A269546 A269547 * A269549 A269550 A269551 KEYWORD sign,easy AUTHOR Michel Marcus, Feb 29 2016 STATUS approved

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Last modified April 22 08:40 EDT 2024. Contains 371893 sequences. (Running on oeis4.)