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 A193716 #25 Oct 25 2017 05:10:18
%S A193716 1,8,7,4,2,6,4,2,2,8,2,8,2,3,1,0,8,0,2,6,4,5,6,9,3,1,2,2,7,3,2,7,5,0,
%T A193716 8,1,2,5,3,0,6,9,0,1,1,7,7,0,3,1,1,5,5,7,0,8,1,0,3,2,6,0,8,3,8,8,1,8,
%U A193716 0,2,3,3,3,1,0,6,2,0,2,8,4,9,7,6,4,9,9,2,3,1,0,6,0,2,4,4,5,8,8,1
%N A193716 Decimal expansion of Pi^3*log(2)/24 - 3*Pi*zeta(3)/16.
%C A193716 The absolute value of the integral {x=0..Pi/2} x^2*log(sin(x )) dx or (d^2/da^2 (integral {x=0..Pi/2} cos(ax)*log(sin(x )) dx)) at a=0. The absolute value of (sum {n=1..infinity} (limit { a -> 0} (d^2/da^2 (sin((a+2n)*Pi/2)/n/(a+2n)))))-(Pi/2)^3*log(2)/3. [_Seiichi Kirikami_ and _Peter J. C. Moses_]
%D A193716 I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, series and Products, 1.441.2, 4th edition, log(sin(x))=-(sum {1..infinity} cos(2nx)/n)-log(2).
%H A193716 R. E. Crandall, J. P. Buhler, <a href="https://projecteuclid.org/euclid.em/1048515810">On the evaluation of Euler sums</a>, Exper. Math. 3 (4) (1994) 275 (discuss int_{0..1} x^n*cot(x) dx which is obtained by partial integration).
%H A193716 S. Koyama and N. Kurokawa, <a href="https://doi.org/10.1090/S0002-9939-04-07863-3">Euler’s integrals and multiple sine functions</a>, Proc. Amer. Math. Soc. 133(2005), 1257-1265.
%F A193716 Equals A091925*A002162/24-3*A000796*A002117/16.
%e A193716 0.18742642282823108026...
%t A193716 RealDigits[ N[Pi (2 Pi^2 Log[2] - 9 Zeta[3]) / 48, 105] ][[1]]
%o A193716 (PARI) Pi^3*log(2)/24 - 3*Pi*zeta(3)/16 \\ _Michel Marcus_, Oct 25 2017
%Y A193716 Cf. A173623, A173624, A193717.
%K A193716 cons,nonn
%O A193716 0,2
%A A193716 _Seiichi Kirikami_, Aug 03 2011