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%I #3 Mar 30 2012 18:51:04
%S 1,41,4927,49277,5913251,33262037,31931555539,127726222157,
%T 4598143997653,306542933176867,827665919577540943,
%U 49659955174652456593,744899327619786848909,1862248319049467122273,446939596571872109345521
%N Numerator of Sum(A159990(k)/A159991(k): 0<=k<=n), denominator=A159993.
%C a(n)/A159993(n) approximates the positive root of x^3+2*x^2+10*x=20:
%C A159994(n)/A159995(n) = f(a(n)/A159993(n)) --> 0,
%C where f(x) = x^3 + 2*x^2 + 10*x - 20;
%C a(n)/A159993(n)=a(n-1)/A159993(n-1))+A159990(n)/A159991(n).
%H R. Zumkeller, <a href="/A159992/b159992.txt">Table of n, a(n) for n = 0..30</a>
%e a(0)/A159993(0) = 1;
%e a(1)/A159993(1) = 41/30;
%e a(2)/A159993(2) = 4927/3600;
%e a(3)/A159993(3) = 49277/36000;
%e a(4)/A159993(4) = 5913251/4320000;
%e a(5)/A159993(5) = 33262037/24300000;
%e a(6)/A159993(6) = 31931555539/23328000000;
%e a(7)/A159993(7) = 127726222157/93312000000;
%e a(8)/A159993(8) = 4598143997653/3359232000000;
%e and written as decimal fractions:
%e a(0)/A159993(0) = 1;
%e a(1)/A159993(1) ~= 1.3666666666666667;
%e a(2)/A159993(2) ~= 1.3686111111111111;
%e a(3)/A159993(3) ~= 1.3688055555555556;
%e a(4)/A159993(4) ~= 1.3688081018518519;
%e a(5)/A159993(5) ~= 1.3688081069958847;
%e a(6)/A159993(6) ~= 1.3688081078103566;
%e a(7)/A159993(7) ~= 1.3688081078210733;
%e a(8)/A159993(8) ~= 1.3688081078213710.
%K frac,nonn
%O 0,2
%A _Reinhard Zumkeller_, May 01 2009
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