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A157701 Decimal expansion of 2*(14*sigma+5)/625 where sigma = sqrt(5)*log(golden ratio). 0
0, 6, 4, 2, 0, 5, 8, 0, 1, 3, 8, 7, 9, 6, 8, 4, 5, 2, 3, 5, 5, 6, 1, 6, 5, 2, 2, 0, 9, 0, 4, 6, 7, 8, 0, 7, 6, 4, 7, 5, 5, 1, 9, 1, 6, 4, 4, 4, 5, 1, 2, 4, 4, 1, 3, 3, 2, 7, 8, 4, 6, 8, 3, 6, 4, 7, 1, 6, 6, 8, 5, 6, 1, 3, 1, 6, 4, 6, 7, 7, 9, 6, 7, 2, 4, 8, 6, 9, 0, 9, 6, 4, 6, 0, 8, 8, 6, 3, 5, 0, 0, 5, 5, 0, 9 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The factor 28 in the Lehmer paper has been corrected to 14.

Equals sum_{n=1..infinity} (-1)^n*n^3/binomial(2n,n).

LINKS

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

D. H. Lehmer, Interesting series involving the Central Binomial Coefficient, Am. Math. Monthly 92, no 7 (1985) 449-457.

R. J. Mathar, Corrigenda to "Interesting series involving...", arXiv:0905.0215

Index entries for transcendental numbers

FORMULA

Equals 2*(14*A002163*A002390+5)/625 .

EXAMPLE

0.064205801387968452355..

MAPLE

2/625*(14*sqrt(5)*log((1+sqrt(5))/2)+5) ;

MATHEMATICA

Join[{0}, RealDigits[2*(14*Sqrt[5]*Log[GoldenRatio]+5)/625, 10, 120][[1]]] (* Harvey P. Dale, Mar 13 2015 *)

PROG

(PARI) 2*(14*sqrt(5)*log((sqrt(5)+1)/2)+5)/625 \\ Charles R Greathouse IV, May 15 2019

CROSSREFS

Cf. A145434, A145433.

Sequence in context: A117254 A211022 A021613 * A193076 A073449 A134300

Adjacent sequences:  A157698 A157699 A157700 * A157702 A157703 A157704

KEYWORD

cons,easy,nonn

AUTHOR

R. J. Mathar, Mar 04 2009

STATUS

approved

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Last modified November 15 18:59 EST 2019. Contains 329149 sequences. (Running on oeis4.)