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 A110191 #32 Feb 16 2025 08:32:58
%S A110191 0,0,7,5,1,1,7,2,3,5,7,4,7,7,1,3,3,0,8,9,7,7,8,2,9,0,3,2,9,4,1,5,2,3,
%T A110191 0,4,6,3,2,2,0,7,0,2,0,9,2,6,2,1,0,2,1,7,9,1,8,9,9,9,3,2,2,6,0,7,7,6,
%U A110191 9,8,6,9,0,3,2,4,4,0,1,3,1,5,7,6,5,5,2,8,6,3,9,0,0,4,1,3,5,8,0,7,1,0
%N A110191 Decimal expansion of 1/6 - 1/(2*Pi).
%D A110191 A. P. Prudnikov, Yu. A. Brychkov, and O. I. Marichev, Integrals and Series, Vol. 1 (Overseas Publishers Association, Amsterdam, 1986), p. 722, section 5.3.5, formula 9.
%H A110191 Bruce C. Berndt and K. Venkatachaliengar, <a href="https://doi.org/10.1007/978-1-4613-0257-5_5">On the transformation formula for the Dedekind eta-function</a>, in: F. G. Garvan and M. E. H. Ismail (eds.), Symbolic Computation, Number Theory, Special Functions, Physics and Combinatorics, eds., Kluwer, Dordrecht, 2001, pp. 73-77; <a href="http://www.math.uiuc.edu/~berndt/articles/venkalatex.pdf">preprint</a>.
%H A110191 Mark W. Coffey, <a href="https://doi.org/10.1016/j.jnt.2017.08.009">Bernoulli identities, zeta relations, determinant expressions, Mellin transforms, and representation of the Hurwitz numbers</a>, Journal of Number Theory, Vol. 184 (2018), pp. 27-67, see Lemma 2, p. 62; <a href="http://arxiv.org/abs/1601.01673">arXiv preprint</a>, arXiv:1601.01673 [math.NT], 2016, see Lemma 2, p. 33.
%H A110191 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/HyperbolicCosecant.html">Hyperbolic Cosecant</a>.
%H A110191 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%F A110191 Equals -Sum_{k>=1} 1/sin(k*Pi*i)^2. - _Michel Marcus_, Jan 11 2016
%F A110191 Equals Sum_{k>=1} 1/sinh(k*Pi)^2. - _Vaclav Kotesovec_, May 19 2022
%e A110191 0.007511723574771330897...
%t A110191 RealDigits[1/6 - 1/(2*Pi), 10, 120, -1][[1]] (* _Amiram Eldar_, Jun 15 2023 *)
%o A110191 (PARI) -1/(2*Pi) + 1/6 \\ _Michel Marcus_, Jan 11 2016
%o A110191 (PARI) -suminf(k=1, 1/sin(k*Pi*I)^2) \\ _Michel Marcus_, Jan 11 2016
%o A110191 (PARI) suminf(k=1, 1/sinh(k*Pi)^2) \\ _Vaclav Kotesovec_, May 19 2022
%Y A110191 Cf. A086201.
%K A110191 nonn,cons
%O A110191 0,3
%A A110191 _Eric W. Weisstein_, Jul 15 2005