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 A246849 #24 Feb 16 2025 08:33:23 %S A246849 8,2,8,4,9,9,5,0,6,8,5,8,4,6,3,9,3,4,1,3,9,5,6,0,0,2,8,4,4,4,7,8,7,8, %T A246849 9,0,3,7,7,7,3,7,0,9,5,7,7,0,4,4,9,1,5,8,2,8,5,7,8,8,9,0,8,1,7,6,3,0, %U A246849 1,3,9,4,4,0,5,6,9,1,4,2,2,0,1,2,0,2,8,8,0,1,9,1,3,1,9,9,1,8,2,6,9 %N A246849 Decimal expansion of 1-delta_0, where delta_0 is the Hall-Montgomery constant (A143301). %C A246849 This constant, by coincidence, is also a limiting probability concerning the number of cycles of a given length in a random permutation. %C A246849 One has P_1(xi) = 1-delta_0 = Pi^2/6 - log(xi) - log(xi)^2 - 2*Li_2(xi), where xi = 1/(1+sqrt(e)) (see A246848 and the references). %H A246849 Steven R. Finch, <a href="http://arxiv.org/abs/2001.00578">Errata and Addenda to Mathematical Constants</a>, arXiv:2001.00578 [math.HO], 2020, p. 29. %H A246849 Michael Lugo, <a href="http://arxiv.org/abs/0909.2909">The number of cycles of specified normalized length in permutations</a>, arXiv:0909.2909 [math.CO], 2009. %H A246849 Eric Weisstein's MathWorld, <a href="https://mathworld.wolfram.com/Hall-MontgomeryConstant.html">Hall-Montgomery Constant</a> %F A246849 Pi^2/6 + log(1 + sqrt(e)) - log(1 + sqrt(e))^2 - 2*Li_2(1/(1 + sqrt(e))), where Li_2 is the dilogarithm function. %e A246849 0.82849950685846393413956002844478789037773709577... %t A246849 Pi^2/6 + Log[1 + Sqrt[E]] - Log[1 + Sqrt[E]]^2 - 2*PolyLog[2, 1/(1 + Sqrt[E])] // RealDigits[#, 10, 101]& // First %o A246849 (PARI) Pi^2/6 + log(exp(1/2)+1) - log(exp(1/2)+1)^2 - 2*polylog(2, 1/(exp(1/2)+1)) \\ _Charles R Greathouse IV_, Sep 08 2014 %o A246849 (Python) %o A246849 from mpmath import mp, log, exp, polylog, pi %o A246849 mp.dps=102 %o A246849 print([int(n) for n in list(str(pi**2/6 + log(exp(1/2)+1) - log(exp(1/2)+1)**2 - 2*polylog(2, 1/(exp(1/2)+1)))[2:-1])]) # _Indranil Ghosh_, Jul 04 2017 %Y A246849 Cf. A143301, A246848. %K A246849 nonn,cons %O A246849 0,1 %A A246849 _Jean-François Alcover_, Sep 05 2014