A268813 Decimal expansion of sum(k>=0, 1/C(k)), where C(k) is a Catalan Number (A000108).

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, 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, 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

Offset

1,1

Links

G. C. Greubel, Table of n, a(n) for n = 1..10000

Eric Weisstein's MathWorld, Catalan Number.

Wikipedia, Catalan number

Formula

Equals 2 + 4*Pi/(9*sqrt(3)) = 1 + A121839.

Also equals 2F1(1, 2; 1/2; 1/4), where 2F1 is the hypergeometric function 2F1.

Example

2.80613305077076348915292367006318032545958499915232914469772663795...

Mathematica

RealDigits[2 + 4*Pi/(9*Sqrt[3]), 10, 102][[1]]

Prog

(PARI) default(realprecision, 100); 2 + 4*Pi/(9*sqrt(3)) \\ G. C. Greubel, Nov 04 2018
(Magma) SetDefaultRealField(RealField(100)); R:=RealField(); 2 + 4*Pi(R)/(9*Sqrt(3)); // G. C. Greubel, Nov 04 2018

Crossrefs

Cf. A000108, A121839 (which is the main entry for this constant).

Sequence in context: A336405 A188924 A011055 * A242056 A195009 A337997

Adjacent sequences: A268810 A268811 A268812 * A268814 A268815 A268816

Keyword

nonn,cons

Author

Jean-François Alcover, Feb 14 2016

Status

approved