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 A204877 Continued fraction expansion of 3*tanh(1/3). 3
 0, 1, 27, 5, 63, 9, 99, 13, 135, 17, 171, 21, 207, 25, 243, 29, 279, 33, 315, 37, 351, 41, 387, 45, 423, 49, 459, 53, 495, 57, 531, 61, 567, 65, 603, 69, 639, 73, 675, 77, 711, 81, 747, 85, 783, 89, 819, 93, 855, 97, 891, 101, 927, 105, 963, 109, 999, 113 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS The continued fraction expansions of tanh(1) and 2*tanh(1/2) are in A004273 and A110185, respectively. LINKS Bruno Berselli, Table of n, a(n) for n = 0..1000 G. Xiao, Contfrac. Index entries for linear recurrences with constant coefficients, signature (0,2,0,-1). FORMULA G.f.: x*(1+27*x+3*x^2+9*x^3)/((1-x)^2*(1+x)^2). E.g.f.: 9-4*exp(-x)*(1+2*x)+5*exp(x)*(-1+2*x). a(n) = (5+4*(-1)^n)*(2*n-1), with a(0)=0. a(n) = 2*a(n-2)-a(n-4) for n>4. a(n) = a(n-2)+A040314(n-2) for n>2. a(n)*a(n+1) = a(2*n^2). Sum(a(i), i=0..n) = A195162(A042948(n)). MATHEMATICA ContinuedFraction[3 Tanh[1/3], 158] CoefficientList[Series[x (1 + 27 x + 3 x^2 + 9 x^3) / ((1 - x)^2 (1 + x)^2), {x, 0, 60}], x] (* Vincenzo Librandi, Jun 14 2013 *) PROG (PARI) \p232;        contfrac(3*tanh(1/3)) (MAGMA) I:=[0, 1, 27, 5, 63]; [n le 5 select I[n] else 2*Self(n-2)-Self(n-4): n in [1..58]]; (Maxima) makelist(coeff(taylor(x*(1+27*x+3*x^2+9*x^3)/((1-x)^2*(1+x)^2), x, 0, n), x, n), n, 0, 57); CROSSREFS Cf. A004273, A110185. Sequence in context: A040714 A040711 A175240 * A040709 A218014 A040710 Adjacent sequences:  A204874 A204875 A204876 * A204878 A204879 A204880 KEYWORD nonn,cofr,easy AUTHOR Bruno Berselli, Jan 23 2012 STATUS approved

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Last modified June 15 17:43 EDT 2019. Contains 324142 sequences. (Running on oeis4.)