OFFSET
0,1
REFERENCES
Jean-Marie Monier, Analyse, Tome 3, 2ème année, MP.PSI.PC.PT, Dunod, 1997, Exercice 3.2.1.q' pp. 247 and 439.
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..25000
Thomas Bloom, Problem 270, Erdős Problems.
Erdős problems database contributors, Erdős problem database, see no. 270.
Simon Plouffe, sum(1/binomial(2n,n), n=1..infinity)
Renzo Sprugnoli, Sums of Reciprocals of the Central Binomial Coefficients, INTEGERS, 6 (2006), #A27, page 9.
Eric Weisstein's World of Mathematics, Central Binomial Coefficient
FORMULA
Equals (9 + 2*sqrt(3)*Pi)/27.
Equals A091682 - 1.
Equals Integral_{x=0..Pi/2} cos(x)/(2 - cos(x))^2 dx. - Amiram Eldar, Aug 19 2020
From Bernard Schott, May 12 2022: (Start)
Equals Sum_{n>=1} (n!)^2 / (2*n)!.
Equals A248179 / 2. (End)
EXAMPLE
0.7363998587187150779097951683649234960631258329094979056821966523...
MATHEMATICA
RealDigits[ N[ (9 + 2*Sqrt[3]*Pi)/27, 110]] [[1]]
PROG
(PARI) (2*Pi*sqrt(3)+9)/27 \\ Michel Marcus, Aug 10 2014
(Magma)
m:= 510; R:=RealField(m); SetDefaultRealField(R);
Prune(Reverse(IntegerToSequence(Floor(( (9 + 2*Sqrt(3)*Pi(R))/27 )*10^(Floor(m/2)) )))); // G. C. Greubel, Sep 09 2025
(SageMath)
numerical_approx( (9 + 2*sqrt(3)*pi)/27 , digits=265 ) # G. C. Greubel, Sep 09 2025
CROSSREFS
KEYWORD
cons,nonn
AUTHOR
Robert G. Wilson v, Aug 03 2002
STATUS
approved