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 A075553 #12 May 09 2014 02:48:20 %S A075553 0,1,-1,1,0,-1,1,-1,0,1,-1,1,0,-1,1,-1,0,1,-1,1,0,-1,1,-1,0,1,-1,1,0, %T A075553 -1,1,-1,0,1,-1,1,0,-1,1,-1,0,1,-1,1,0,-1,1,-1,0,1,-1,1,0,-1,1,-1,0,1, %U A075553 -1,1,0,-1,1,-1,0,1,-1,1,0,-1,1,-1,0,1,-1,1,0,-1,1,-1,0,1,-1,1,0,-1,1,-1,0,1,-1,1,0,-1,1,-1,0,1,-1,1,0,-1,1,-1,0 %N A075553 Numerators in the Maclaurin series for arctan(1+x). %F A075553 Euler transform of length 8 sequence [ -1, 1, 1, -1, 0, -1, 0, 1]. - _Michael Somos_, Jul 16 2006 %F A075553 G.f.: x(1-x+x^2)/(1+x^4) = x(1-x)(1-x^4)(1-x^6)/((1-x^2)(1-x^3)(1-x^8)). a(-n) = a(n+4) = -a(n). - _Michael Somos_, Jul 16 2006 %t A075553 a[n_] := I ((-1 - I)^n - (-1 + I)^n)/2^Floor[1 + n/2]; Table[a[n], {n, 0, 100}] %o A075553 (PARI) a(n)=[0,1,-1,1,0,-1,1,-1][n%8+1] /* _Michael Somos_, Jul 16 2006 */ %Y A075553 Cf. A075554. %K A075553 sign,easy %O A075553 0,1 %A A075553 _Eric W. Weisstein_, Sep 23 2002