A221209 Decimal expansion of two times the Catalan constant.

1, 8, 3, 1, 9, 3, 1, 1, 8, 8, 3, 5, 4, 4, 3, 8, 0, 3, 0, 1, 0, 9, 2, 0, 7, 0, 2, 9, 8, 6, 4, 7, 6, 8, 2, 2, 1, 5, 4, 8, 2, 9, 8, 7, 4, 8, 5, 6, 3, 3, 4, 4, 2, 6, 8, 5, 3, 2, 9, 9, 6, 2, 3, 9, 2, 4, 3, 5, 2, 6, 0, 3, 9, 5, 5, 2, 5, 0, 9, 5, 3, 8, 9, 5, 8, 7, 1, 3, 0, 2, 5, 8, 5, 2, 2, 3, 0, 2, 1, 2

Offset

1,2

References

I.S. Gradshteyn and I.M. Ryzhik, Table of integrals, series and products, 5th edition, Academic Press, 1994, eq. (3.521.2).

Links

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

Formula

Equals Integral_{x=0..oo} x/cosh(x) dx.

Equals 2*A006752.

From Amiram Eldar, Aug 20 2020: (Start)

Equals Integral_{x=0..Pi/2} x/sin(x) dx.

Equals 1 + Integral_{x=0..oo} x * exp(-x) * tanh(x) dx. (End)

Example

1.83193118835443803010920702986476822154...

Maple

evalf(2*Catalan) ;

Mathematica

RealDigits[2 Catalan, 10, 100][[1]] (* Bruno Berselli, Feb 21 2013 *)

Prog

(PARI) default(realprecision, 100); 2*Catalan \\ G. C. Greubel, Aug 25 2018
(Magma) SetDefaultRealField(RealField(100)); R:=RealField(); 2*Catalan(R); // G. C. Greubel, Aug 25 2018

Crossrefs

Cf. A006752.

Sequence in context: A097890 A088453 A019782 * A056030 A364889 A195473

Adjacent sequences: A221206 A221207 A221208 * A221210 A221211 A221212

Keyword

nonn,cons,easy

Author

R. J. Mathar, Feb 21 2013

Status

approved