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 A225746 #20 Feb 16 2025 08:33:19
%S A225746 0,2,4,8,7,5,4,4,7,7,0,3,3,7,8,4,2,6,2,5,4,7,2,5,2,9,9,3,5,7,6,1,1,3,
%T A225746 9,7,6,0,9,7,3,6,9,7,1,3,6,6,8,5,3,5,1,1,6,9,9,9,8,5,5,6,3,9,6,9,0,6,
%U A225746 9,3,0,3,2,9,9,9,9,1,0,5,0,6,0,9,2,8,5,8,4,3,3,6,6,5,8,4,2,0,8,8,8
%N A225746 Decimal expansion of the logarithm of Glaisher's constant.
%D A225746 Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 2.15 Glaisher-Kinkelin constant, p. 135.
%H A225746 Jesús Guillera and Jonathan Sondow, <a href="https://doi.org/10.1007/s11139-007-9102-0">Double integrals and infinite products for some classical constants via analytic continuations of Lerch's transcendent</a>, The Ramanujan Journal, Vol. 16, No. 3 (2008), pp. 247-270; <a href="https://arxiv.org/abs/math/0506319">arXiv preprint</a>, arXiv:math/0506319 [math.NT], 2005-2006.
%H A225746 Jean-Christophe Pain, <a href="https://arxiv.org/abs/2405.05264">Two integral representations for the logarithm of the Glaisher-Kinkelin constant</a>, arXiv:2405.05264 [math.GM], 2024.
%H A225746 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Glaisher-KinkelinConstant.html">Glaisher-Kinkelin Constant</a>.
%F A225746 Equals 1/12 - zeta'(-1).
%F A225746 Also equals (gamma + log(2*Pi))/12 -zeta'(2)/(2*Pi^2).
%F A225746 From _Amiram Eldar_, Apr 15 2021: (Start)
%F A225746 Equals lim_{n->oo} (Sum_{k=1..n} k*log(k) - (n^2/2 + n/2 + 1/12)*log(n) + n^2/4).
%F A225746 Equals 1/8 + (1/2) * Sum_{n>=0} ((1/(n+1)) * Sum_{k=0..n} (-1)^(k+1) * binomial(n,k) * (k+1)^2 * log(k+1)) (Guillera and Sondow, 2008). (End)
%e A225746 0.248754477033784262547252993576113976097369713668535116999855639690693032999...
%t A225746 RealDigits[Log[Glaisher], 10, 100] // First
%o A225746 (PARI) 1/12-zeta'(-1) \\ _Charles R Greathouse IV_, Dec 12 2013
%Y A225746 Cf. A001620, A073002, A074962, A084448.
%K A225746 nonn,cons
%O A225746 1,2
%A A225746 _Jean-François Alcover_, May 14 2013