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 A085568 #4 Mar 30 2012 16:49:45 %S A085568 1,2,8,4,88,28,104,376,1904,372,30152,4952,193072,245848,64304,7984, %T A085568 8303392,32131172,126932136,164384184,185914544,16850280,3006076208, %U A085568 249890288,5554299808,21745428728,9598969456,37645191344,5687521456416,378608431568,4518712438048 %N A085568 Numerator of 2*Sum(C(n,w)/(2*w+1),w=0..n/2-1)+C(n,n/2)/(n+1) if n is even, or of 2*Sum(C(n,w)/(2*w+1),w=0..(n-1)/2) if n is odd. %e A085568 1, 2, 8/3, 4, 88/15, 28/3, 104/7, 376/15, 1904/45, 372/5, 30152/231, ... %p A085568 b := binomial; f1 := n->if n mod 2 = 0 then 2*add(b(n,w)/(2*w+1),w=0..n/2-1)+b(n,n/2)/(n+1); else 2*add(b(n,w)/(2*w+1),w=0..(n-1)/2); fi; %Y A085568 Cf. A085569-A086673. %K A085568 nonn,frac %O A085568 0,2 %A A085568 _N. J. A. Sloane_, Jul 07 2003