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%I #47 Jun 09 2023 08:02:43
%S 7,3,6,3,9,9,8,5,8,7,1,8,7,1,5,0,7,7,9,0,9,7,9,5,1,6,8,3,6,4,9,2,3,4,
%T 9,6,0,6,3,1,2,5,8,3,2,9,0,9,4,9,7,9,0,5,6,8,2,1,9,6,6,5,2,3,0,8,4,7,
%U 1,8,1,8,0,2,8,0,7,8,6,4,0,8,1,8,6,9,4,4,4,1,8,2,4,9,0,2,2,5,9,7,4,5,8,2,7
%N Decimal expansion of Sum_{n>=1} 1/binomial(2n,n).
%D Jean-Marie Monier, Analyse, Tome 3, 2ème année, MP.PSI.PC.PT, Dunod, 1997, Exercice 3.2.1.q' pp. 247 and 439.
%H Simon Plouffe, <a href="http://www.worldwideschool.org/library/books/sci/math/MiscellaneousMathematicalConstants/chap85.html">sum(1/binomial(2n,n), n=1..infinity)</a>
%H Renzo Sprugnoli, <a href="http://www.emis.de/journals/INTEGERS/papers/g27/g27.Abstract.html">Sums of Reciprocals of the Central Binomial Coefficients</a>, INTEGERS, 6 (2006), #A27, page 9.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/CentralBinomialCoefficient.html">Central Binomial Coefficient</a>
%F Equals (9 + 2*sqrt(3)*Pi)/27.
%F Equals A091682 - 1.
%F Equals Integral_{x=0..Pi/2} cos(x)/(2 - cos(x))^2 dx. - _Amiram Eldar_, Aug 19 2020
%F From _Bernard Schott_, May 12 2022: (Start)
%F Equals Sum_{n>=1} (n!)^2 / (2*n)!.
%F Equals A248179 / 2. (End)
%e 0.7363998587187150779097951683649234960631258329094979056821966523...
%t RealDigits[ N[ (9 + 2*Sqrt[3]*Pi)/27, 110]] [[1]]
%o (PARI) (2*Pi*sqrt(3)+9)/27 \\ _Michel Marcus_, Aug 10 2014
%Y Cf. A000984 (central binomial coefficients), A091682, A248179.
%K cons,nonn
%O 0,1
%A _Robert G. Wilson v_, Aug 03 2002
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