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 A222183 #41 Nov 12 2024 17:23:11
%S A222183 1,0,7,4,8,3,3,0,7,2,1,5,6,6,9,4,4,2,1,2,0,4,4,5,7,4,4,4,9,5,8,4,5,1,
%T A222183 5,0,1,3,4,4,1,8,0,9,0,0,0,9,3,3,8,5,4,8,1,2,8,4,0,8,3,3,9,5,8,2,4,6,
%U A222183 3,4,3,1,1,2,8,9,3,2,7,7,1,2,4,2,7,2,8
%N A222183 Decimal expansion of Sum_{k >= 0} 1/(4*k+1)^2.
%D A222183 Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 1.7.2, p. 55.
%H A222183 Vincenzo Librandi, <a href="/A222183/b222183.txt">Table of n, a(n) for n = 1..5000</a>
%H A222183 E. D. Krupnikov and K. S. Kolbig, <a href="https://dx.doi.org/10.1016/S0377-0427(96)00111-2">Some special cases of the generalized hypergeometric function (q+1)Fq</a>, J. Comp. Appl. Math. 78 (1997) 79-95.
%H A222183 Michael I. Shamos, <a href="http://euro.ecom.cmu.edu/people/faculty/mshamos/cat.pdf">A catalog of the real numbers</a>, (2007). See p. 112.
%F A222183 Equals A006752/2 + A222068.
%F A222183 Equals -Integral_{x=0..1} log(x)/(1 - x^4) dx. - _Amiram Eldar_, Jul 17 2020
%F A222183 Equals 3F2(1/4,1/4,1;5/4,5/4;1). [Krupnikov] - _R. J. Mathar_, Jun 12 2024
%F A222183 Equals psi'(1/4)/16 (see Shamos). - _Stefano Spezia_, Nov 12 2024
%e A222183 1.074833072156694421204457444958451501344... = 1 + 1/25 + 1/81 + 1/169 + 1/289 + ...
%t A222183 RealDigits[Catalan/2 + Pi^2/16, 10, 90][[1]] (* or *) RealDigits[PolyGamma[1, 1/4]/16, 10, 90]
%o A222183 (PARI) (8*Catalan + Pi^2)/16 \\ _G. C. Greubel_, Aug 23 2018
%o A222183 (Magma) SetDefaultRealField(RealField(100)); R:= RealField(); (8*Catalan(R) + Pi(R)^2)/16; // _G. C. Greubel_, Aug 23 2018
%Y A222183 Cf. A006752, A222068.
%Y A222183 Cf. A013661, A111003, A214550.
%K A222183 nonn,cons
%O A222183 1,3
%A A222183 _Bruno Berselli_, Feb 11 2013