This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A253191 #31 May 27 2025 16:40:29
%S A253191 4,8,0,4,5,3,0,1,3,9,1,8,2,0,1,4,2,4,6,6,7,1,0,2,5,2,6,3,2,6,6,6,4,9,
%T A253191 7,1,7,3,0,5,5,2,9,5,1,5,9,4,5,4,5,5,8,6,8,6,6,8,6,4,1,3,3,6,2,3,6,6,
%U A253191 5,3,8,2,2,5,9,8,3,4,4,7,2,1,9,9,9,4,8,2,6,3,4,4,3,9,2,6,9,9,0,9,3,2,7
%N A253191 Decimal expansion of log(2)^2.
%H A253191 David H. Bailey, Jonathan M. Borwein and Richard E. Crandall, <a href="https://doi.org/10.1090/S0025-5718-97-00800-4">On the Khintchine Constant</a>, Mathematics of Computation, Vol. 66, No. 217 (1997), pp. 417-431, see p. 419; <a href="http://www.davidhbailey.com/dhbpapers/khinchine.pdf">alternative link</a>, p. 4.
%H A253191 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>
%F A253191 Integral_{0..1} log(1-x^2)/(x*(1+x)) dx = -log(2)^2.
%F A253191 Integral_{0..1} log(log(1/x))/(x+sqrt(x)) dx = log(2)^2.
%F A253191 Equals Sum_{k>=1} H(k)/(2^k * (k+1)) = 2 * Sum_{k>=1} (-1)^(k+1) * H(k)/(k+1), where H(k) = A001008(k)/A002805(k) is the k-th harmonic number. - _Amiram Eldar_, Aug 05 2020
%F A253191 Equals Sum_{n >= 0} (-1)^n/(2^(n+1)*(n+1)^2*binomial(2*n+1,n)). See my entry in A002544 dated Apr 18 2017. Cf. A091476. - _Peter Bala_, Jan 30 2023
%F A253191 Equals 2*Integral_{x=-1..1} (abs(x)*log(x^2 + 1))/(x^2 + 1) dx. - _Kritsada Moomuang_, May 27 2025
%e A253191 0.480453013918201424667102526326664971730552951594545586866864...
%t A253191 RealDigits[Log[2]^2, 10, 103] // First
%o A253191 (PARI) log(2)^2 \\ _Charles R Greathouse IV_, Apr 20 2016
%Y A253191 Cf. A001008, A002162, A002805, A175478.
%K A253191 nonn,cons,easy
%O A253191 0,1
%A A253191 _Jean-François Alcover_, Mar 24 2015