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%I #18 Aug 10 2020 10:35:22
%S 23,24,71,95,261,6098,12457,18555,49567,68122,3183179,3251301,9685781,
%T 12937082,35559945,830815817,1697191579,2528007396,6753206371,
%U 9281213767,433689039653,442970253420,1319629546493,1762599799913,4844829146319
%N Numerators of continued fraction convergents to sqrt(563).
%H Vincenzo Librandi, <a href="/A042078/b042078.txt">Table of n, a(n) for n = 0..200</a>
%H <a href="/index/Rec#order_20">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 0, 0, 0, 0, 0, 0, 0, 136244, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1).
%F G.f.: (23 +24*x +71*x^2 +95*x^3 +261*x^4 +6098*x^5 +12457*x^6 +18555*x^7 +49567*x^8 +68122*x^9 +49567*x^10 -18555*x^11 +12457*x^12 -6098*x^13 +261*x^14 -95*x^15 +71*x^16 -24*x^17 +23*x^18 -x^19)/(1 -136244*x^10 +x^20). [_Bruno Berselli_, Nov 15 2013]
%t Numerator[Convergents[Sqrt[563], 30]] (* _Vincenzo Librandi_, Nov 15 2013 *)
%t CoefficientList[Series[(23 + 24 x + 71 x^2 + 95 x^3 + 261 x^4 + 6098 x^5 + 12457 x^6 + 18555 x^7 + 49567 x^8 + 68122 x^9 + 49567 x^10 - 18555 x^11 + 12457 x^12 - 6098 x^13 + 261 x^14 - 95 x^15 + 71 x^16 - 24 x^17 + 23 x^18 - x^19)/(1 - 136244 x^10 + x^20), {x, 0, 30}], x] (* _Bruno Berselli_, Nov 15 2013 *)
%t LinearRecurrence[{0,0,0,0,0,0,0,0,0,136244,0,0,0,0,0,0,0,0,0,-1},{23,24,71,95,261,6098,12457,18555,49567,68122,3183179,3251301,9685781,12937082,35559945,830815817,1697191579,2528007396,6753206371,9281213767},20] (* _Harvey P. Dale_, Aug 10 2020 *)
%Y Cf. A042079.
%K nonn,cofr,frac,easy,less
%O 0,1
%A _N. J. A. Sloane_.
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