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 A194656 #25 Jul 14 2025 22:52:30
%S A194656 1,2,2,0,4,7,2,9,5,8,8,5,9,2,8,7,2,1,6,3,3,2,6,0,2,9,6,2,8,2,2,9,5,2,
%T A194656 8,8,1,4,4,5,6,8,7,2,0,5,0,5,6,9,2,4,2,8,1,5,5,4,3,8,5,7,9,2,6,4,2,7,
%U A194656 6,2,1,5,6,7,7,7,9,5,5,8,6,5,2,1,0,9,1,3,5,3,0,9,5,5,0,4,5,5,8,2,8,0,9,3,5
%N A194656 Decimal expansion of (2*Pi^5*log(2) - 30*Pi^3*zeta(3) + 225*Pi*zeta(5))/320.
%C A194656 The absolute value of the integral{x=0..Pi/2} x^4*log(sin(x )) dx or(d^4/da^4(integral {x=0..Pi/2} cos(ax)*log(sin(x )) dx)) at a=0. The absolute value of m=2 of (-1)^(m+1)*(sum {n=1..infinity} (limit {a -> 0} (d^(2m)/da^(2m)(sin((a+2n)*Pi/2)/n/(a+2n)))))-(Pi/2)^(2m+1)*log(2)/(2m+1). - _Seiichi Kirikami_ and _Peter J. C. Moses_, Sep 01 2011
%D A194656 I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series and Products, 4th edition, 1.441.2
%F A194656 Equals (2*A092731*A002162-30*A091925*A002117+225*A000796*A013663)/320.
%e A194656 0.12204729588592872163...
%t A194656 RealDigits[ N[Pi (2 Pi^4*Log[2]-30 Pi^2*Zeta[3]+225 Zeta[5])/320, 150]][[1]]
%Y A194656 Cf. A173623, A173624, A193716, A193717.
%K A194656 cons,nonn
%O A194656 0,2
%A A194656 _Seiichi Kirikami_, Sep 01 2011