A086465 Decimal expansion of (5 + 4*sqrt(5)*arcsch(2))/25.

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

Offset

0,1

Links

G. C. Greubel, Table of n, a(n) for n = 0..20000

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.

Index entries for transcendental numbers.

Formula

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

Example

0.3721635763856016155557732931802421701698282730161158619...

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
(Magma)
m:= 510; SetDefaultRealField(RealField(m));
A086465:= (5+ 4*Sqrt(5)*Argsinh(1/2))/25;
Prune(Reverse(IntegerToSequence(Floor(( A086465 )*10^(Floor(m/2)) )))); // G. C. Greubel, Nov 29 2025
(SageMath)
A086465= numerical_approx( (5 + 4*sqrt(5)*asinh(1/2))/25, digits= 250)
print([ZZ(i) for i in A086465.str()[1:-5] if i.isdigit()]) # G. C. Greubel, Nov 29 2025

Crossrefs

Cf. A086466, A086467, A086468.

Sequence in context: A016451 A093097 A343201 * A378077 A182502 A059818

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