A086465 - OEIS

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A086465

Decimal expansion of (5 + 4*sqrt(5)*arcsch(2))/25.

5

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

(list; constant; graph; refs; listen; history; text; internal format)

OFFSET

0,1

LINKS

Table of n, a(n) for n=0..98.

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

Eric Weisstein's World of Mathematics, Central Binomial Coefficient.

Wikipedia, Inverse hyperbolic function: Series expansions.

FORMULA

Equals Sum_{n>=1} (-1)^(n-1)/binomial(2*n,n).

EXAMPLE

0.37216357638560161555577...

MAPLE

2/625*(14*sqrt(5)*log((1+sqrt(5))/2)+5) ; # R. J. Mathar, Mar 04 2009

MATHEMATICA

RealDigits[(5 + 4*Sqrt[5]*ArcSinh[1/2])/25, 10, 120][[1]] (* Amiram Eldar, May 25 2023 *)

PROG

(PARI) suminf(n=1, (-1)^(n-1)/binomial(2*n, n)) \\ Michel Marcus, Jul 31 2015

(PARI) asinh(.5)*sqrt(5)*.16+.2 \\ Use \p99 to get 99 digits. - M. F. Hasler, Jul 31 2015

CROSSREFS

Cf. A086466, A086467, A086468.

Sequence in context: A016451 A093097 A343201 * A182502 A059818 A374829

Adjacent sequences: A086462 A086463 A086464 * A086466 A086467 A086468

KEYWORD

nonn,cons

AUTHOR

Eric W. Weisstein, Jul 21 2003

EXTENSIONS

Corrected definition and digits by a factor of 25/24. - R. J. Mathar, Mar 04 2009

STATUS

approved