|
%I #15 Sep 08 2022 08:46:15
%S 2,8,0,6,1,3,3,0,5,0,7,7,0,7,6,3,4,8,9,1,5,2,9,2,3,6,7,0,0,6,3,1,8,0,
%T 3,2,5,4,5,9,5,8,4,9,9,9,1,5,2,3,2,9,1,4,4,6,9,7,7,2,6,6,3,7,9,5,0,2,
%U 7,6,9,6,9,3,8,9,4,9,0,6,1,4,9,7,0,7,2,2,2,1,6,9,8,3,1,3,7,8,5,2,8,2
%N Decimal expansion of sum(k>=0, 1/C(k)), where C(k) is a Catalan Number (A000108).
%H G. C. Greubel, <a href="/A268813/b268813.txt">Table of n, a(n) for n = 1..10000</a>
%H Eric Weisstein's MathWorld, <a href="http://mathworld.wolfram.com/CatalanNumber.html">Catalan Number</a>.
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Catalan_number">Catalan number</a>
%F Equals 2 + 4*Pi/(9*sqrt(3)) = 1 + A121839.
%F Also equals 2F1(1, 2; 1/2; 1/4), where 2F1 is the hypergeometric function 2F1.
%e 2.80613305077076348915292367006318032545958499915232914469772663795...
%t RealDigits[2 + 4*Pi/(9*Sqrt[3]), 10, 102][[1]]
%o (PARI) default(realprecision, 100); 2 + 4*Pi/(9*sqrt(3)) \\ _G. C. Greubel_, Nov 04 2018
%o (Magma) SetDefaultRealField(RealField(100)); R:=RealField(); 2 + 4*Pi(R)/(9*Sqrt(3)); // _G. C. Greubel_, Nov 04 2018
%Y Cf. A000108, A121839 (which is the main entry for this constant).
%K nonn,cons
%O 1,1
%A _Jean-François Alcover_, Feb 14 2016
|
