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 A215746 #25 Feb 16 2025 08:33:18
%S A215746 4,8,52,304,1052,10312,147916,135904,2490548,44257352,47028692,
%T A215746 1023461776,5385020324,15411418072,467009482388,13895021563328,
%U A215746 14442004718228,13926277743608,533322720625196,516197940314096,21831981985010836,911392701638017048,937558224301357108
%N A215746 Numerator of Sum_{i=0..n} (-1)^i*4/(2*i + 1).
%C A215746 Denominator of the sum divides A025547(n+1), but is not always equal to it: the first exception is n = 32.
%C A215746 x(n) = Sum_{i=0..n} (-1)^i*4/(2*i+1) very slowly converges to Pi, with x(n) > Pi when n is even and x(n) < Pi when n is odd.
%H A215746 Robert Israel, <a href="/A215746/b215746.txt">Table of n, a(n) for n = 0..229</a>
%H A215746 Eric W. Weisstein, <a href="https://mathworld.wolfram.com/PiFormulas.html">MathWorld: Pi formulas</a>
%e A215746 a(2) = 52 because 4 - 4/3 + 4/5 = 60/15 - 20/15 + 12/15 = 52/15.
%p A215746 N:= 100; # to get terms up to a[N]
%p A215746 T[0]:= 4;
%p A215746 A215746[0]:= 4;
%p A215746 for i from 1 to N do
%p A215746 T[i]:= T[i-1] + (-1)^i*4/(2*i+1);
%p A215746 A215746[i]:= numer(T[i])
%p A215746 od:
%p A215746 [seq](A215746[i],i=0..N); # _Robert Israel_, Apr 27 2014
%t A215746 Table[Numerator[Sum[(-1)^i 4/(2i + 1), {i, 0, n}]], {n, 0, 39}]
%Y A215746 Cf. A007509.
%K A215746 nonn,easy,frac
%O A215746 0,1
%A A215746 _Alonso del Arte_, Aug 22 2012
%E A215746 Definition and comments corrected by _Robert Israel_, Apr 27 2014