A073016 Decimal expansion of Sum_{n>=1} 1/binomial(2n,n).

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, 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, 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

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

Table of n, a(n) for n=0..104.

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

Crossrefs

Cf. A000984 (central binomial coefficients), A091682, A248179.

Sequence in context: A246203 A354627 A091682 * A238695 A019819 A215693

Adjacent sequences: A073013 A073014 A073015 * A073017 A073018 A073019

Keyword

cons,nonn

Author

Robert G. Wilson v, Aug 03 2002

Status

approved