A086467 - OEIS

%I #24 Nov 21 2024 08:09:37

%S 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,

%T 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,

%U 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

%N Decimal expansion of 2*arccsch(2)^2.

%H Steven R. Finch, <a href="https://doi.org/10.1017/9781316997741">Mathematical Constants II</a>, Encyclopedia of Mathematics and Its Applications, Cambridge University Press, Cambridge, 2018, p. 77.

%H Renzo Sprugnoli, <a href="https://www.emis.de/journals/INTEGERS/papers/g27/g27.Abstract.html">Sums of reciprocals of the central binomial coefficients</a>, INTEGERS 6 (2006) #A27

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/CentralBinomialCoefficient.html">Central Binomial Coefficient</a>

%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>

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

%F Equals Integral_{x=0..1} log(1+x-x^2)/x dx. - _Vaclav Kotesovec_, Jun 13 2021

%F Equals 2*A002390^2. - _R. J. Mathar_, Jun 07 2024

%e 0.4631296...

%t RealDigits[2ArcCsch[2]^2,10,120][[1]] (* _Harvey P. Dale_, Mar 07 2012 *)

%o (PARI) suminf(n=1, (-1)^(n-1)/n^2/binomial(2*n,n)) \\ _Michel Marcus_, Jul 31 2015

%o (PARI) 2*asinh(.5)^2 \\ _Charles R Greathouse IV_, Nov 21 2024

%Y Cf. A086465, A086466, A086468.

%K nonn,cons

%O 0,1

%A _Eric W. Weisstein_, Jul 21 2003