A086467 Decimal expansion of 2*arccsch(2)^2.

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

Offset

0,1

Links

Table of n, a(n) for n=0..101.

Steven R. Finch, Mathematical Constants II, Encyclopedia of Mathematics and Its Applications, Cambridge University Press, Cambridge, 2018, p. 77.

Renzo Sprugnoli, Sums of reciprocals of the central binomial coefficients, INTEGERS 6 (2006) #A27

Eric Weisstein's World of Mathematics, Central Binomial Coefficient

Index entries for transcendental numbers

Formula

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

Equals Integral_{x=0..1} log(1+x-x^2)/x dx. - Vaclav Kotesovec, Jun 13 2021

Equals 2*A002390^2. - R. J. Mathar, Jun 07 2024

Example

0.4631296...

Mathematica

RealDigits[2ArcCsch[2]^2, 10, 120][[1]] (* Harvey P. Dale, Mar 07 2012 *)

Prog

(PARI) suminf(n=1, (-1)^(n-1)/n^2/binomial(2*n, n)) \\ Michel Marcus, Jul 31 2015
(PARI) 2*asinh(.5)^2 \\ Charles R Greathouse IV, Nov 21 2024

Crossrefs

Cf. A086465, A086466, A086468.

Sequence in context: A182368 A185442 A204174 * A197731 A325009 A325017

Adjacent sequences: A086464 A086465 A086466 * A086468 A086469 A086470

Keyword

nonn,cons,changed

Author

Eric W. Weisstein, Jul 21 2003

Status

approved