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 A128500 #11 Sep 20 2024 03:20:55
%S A128500 1,1,1,3,11,11,97,159,159,187,1777,1777,26181,23321,23321,51647,
%T A128500 797919,797919,16521821,15228529,15228529,16404249,351431887,
%U A128500 351431887,1876142299,1761735699,1761735699,1867970399,51196569971,51196569971
%N A128500 Numerators of partial sums for a series for Pi/(3*sqrt(3)).
%C A128500 The denominators are given in A128501.
%C A128500 The limit n -> infinity of the rationals r(n) defined below is Pi/(3*sqrt(3)).
%H A128500 W. Lang, <a href="/A128500/a128500.txt">Rationals and limit.</a>
%F A128500 a(n)=numerator(r(n)) with the rationals r(n):=Sum_{k=0..n} ((-1)^k)*S(k,1)/(k+1) with Chebyshev's S-Polynomials S(k,1)=[1,1,0,-1,-1,0] periodic sequence with period 6. See A010892.
%e A128500 Rationals: [1, 1/2, 1/2, 3/4, 11/20, 11/20, 97/140, 159/280, 159/280, 187/280,...]
%e A128500 Pi/(3*sqrt(3))=+1/1 -1/2 +1/4 -1/5 +1/7 -1/8 +1/10 -1/11 +1/13 -+
%K A128500 nonn,frac,easy
%O A128500 0,4
%A A128500 _Wolfdieter Lang_ Apr 04 2007