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A276483 Decimal expansion of Sum_{k>=0} (2*k+1)/binomial(4*k,2*k). 0
1, 5, 7, 9, 7, 6, 8, 3, 7, 9, 5, 5, 4, 0, 2, 0, 7, 7, 5, 2, 4, 2, 9, 9, 7, 8, 5, 9, 1, 2, 3, 4, 4, 4, 8, 6, 0, 6, 2, 7, 8, 9, 5, 5, 3, 5, 7, 6, 6, 4, 9, 5, 0, 5, 5, 2, 0, 7, 1, 8, 1, 8, 5, 4, 0, 1, 6, 9, 2, 3, 7, 9, 2, 9, 8, 4, 0, 7, 3, 6, 3, 6, 7, 5, 8, 6, 0, 3, 4, 4, 4, 9, 6, 4, 2, 3, 6, 1, 3, 7, 1, 1, 4, 9, 7, 4, 5, 3, 9, 6, 1, 6, 7, 0, 3, 2, 1, 3, 2, 7 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..120.

Eric Weisstein's MathWorld, Catalan Number

FORMULA

Equals 2*Pi/(9*sqrt(3)) - 4*(3*sqrt(5)*log(phi) - 40)/125, where phi is the golden ratio (A001622).

Equals Sum_{k>=0} 1/Catalan number(2k).

Equals Sum_{k>=0} 1/A000108(2k).

Equals Sum_{k>=0} 1/A048990(k).

EXAMPLE

1.57976837955402077524299785912344486...

MATHEMATICA

RealDigits[2 (Pi/(9 Sqrt[3])) - 4 ((3 Sqrt[5] Log[GoldenRatio] - 40)/125), 10, 120][[1]]

RealDigits[HypergeometricPFQ[{1, 1, 3/2}, {1/4, 3/4}, 1/16], 10, 120][[1]]

PROG

(PARI) suminf(k=0, 1/(binomial(4*k, 2*k)/(2*k+1))) \\ Michel Marcus, Sep 06 2016

CROSSREFS

Cf. A000108, A001622, A048990, A121839, A268813.

Sequence in context: A068456 A239097 A153612 * A021637 A177705 A135913

Adjacent sequences:  A276480 A276481 A276482 * A276484 A276485 A276486

KEYWORD

nonn,cons

AUTHOR

Ilya Gutkovskiy, Sep 05 2016

STATUS

approved

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Last modified February 18 04:10 EST 2018. Contains 299298 sequences. (Running on oeis4.)