|
%I #14 Jan 15 2018 15:46:35
%S 2,3,-24,-81,160,1215,-896,-15309,4608,177147,-22528,-1948617,106496,
%T 20726199,-491520,-215233605,2228224,2195382771,-9961472,-22082967873,
%U 44040192,219667417263,-192937984,-2165293113021,838860800
%N Egyptian fraction expansion for Pi/4 = arctan(1/2) + arctan(1/3) (Hutton 1776).
%C Sum_{n>=0} 1/a(n) = Pi/4.
%H Vincenzo Librandi, <a href="/A157327/b157327.txt">Table of n, a(n) for n = 0..1000</a>
%H X. Gourdon and P. Sebah, <a href="http://numbers.computation.free.fr/Constants/Pi/piclassic.html">The constant Pi. The classic period</a>
%F G.f.: 2*(1-4*x^2)/(1+4*x^2)^2 + 3*x*(1-9*x^2)/(1+9*x^2)^2.
%t CoefficientList[Series[2 (1 - 4 x^2)/(1 + 4 x^2)^2 + 3 x (1 - 9 x^2)/(1 + 9 x^2)^2, {x, 0, 40}], x] (* _Vincenzo Librandi_, Dec 12 2012 *)
%Y Cf. A157142, A155988, A058962.
%K frac,sign
%O 0,1
%A _Jaume Oliver Lafont_, Feb 27 2009
|
