%I #13 Oct 14 2017 10:44:14
%S 60,23940,9528120,3792167880,1509273288180,600686976527820,
%T 239071907384784240,95150018452167599760,37869468272055319920300,
%U 15071953222259565160679700,5998599512991034878630600360,2387427534217209622129818263640,950190160018936438572789038328420
%N Coefficients of the series giving the best rational approximations to sqrt(11).
%C The partial sums of the series 10/3 - 1/a(1) - 1/a(2) - 1/a(3) - ... give the best rational approximations to sqrt(11), which constitute every second convergent of the continued fraction. The corresponding continued fractions are [3;3,6,3], [3;3,6,3,6,3], [3;3,6,3,6,3,6,3] and so forth.
%H G. C. Greubel, <a href="/A123482/b123482.txt">Table of n, a(n) for n = 1..380</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (399,-399,1).
%F a(n+3) = 399*a(n+2) - 399*a(n+1) + a(n).
%F a(n) = -5/33 + (5/66 + 1/44*11^(1/2))*(199 + 60*11^(1/2))^n + (5/66 - 1/44*11^(1/2))*(199 - 60*11^(1/2))^n.
%F G.f.: -60*x / ((x-1)*(x^2-398*x+1)). - _Colin Barker_, Jun 23 2014
%t CoefficientList[Series[-60*x/((x - 1)*(x^2 - 398*x + 1)), {x, 0, 50}], x] (* _G. C. Greubel_, Oct 13 2017 *)
%o (PARI) Vec(-60*x/((x-1)*(x^2-398*x+1)) + O(x^100)) \\ _Colin Barker_, Jun 23 2014
%Y Cf. A010468, A041014, A041015.
%Y Cf. A123478, A123479, A123480, A029549.
%K nonn,easy
%O 1,1
%A _Gene Ward Smith_, Oct 02 2006
%E More terms from _Colin Barker_, Jun 23 2014