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%I #27 Feb 28 2023 13:07:19
%S 0,-2,1,1,1,5,7,7,33,429,715,2431,4199,29393,52003,185725,111435,
%T 1938969,17678835,21607465,119409675,883631595,109402007,6116566755,
%U 11435320455,57176602275,322476036831,1215486600363,2295919134019
%N Numerators of coefficients of 1/2^(2n+1) in Newton's series for Pi.
%C According to Beckmann, Newton undertook his Pi calculations in Woolsthorpe during the plague years of 1665-6. Actually, Newton was calculating something else, and Pi appeared only as an incidental fringe benefit in the calculation. Twenty-two terms were sufficient to give him 16 decimal places (the last was incorrect because of the inevitable error in rounding off). - _Johannes W. Meijer_, Feb 23 2013
%D Petr Beckmann, A history of Pi, 1974, pp. 140-143.
%H A. Sofo, <a href="http://www.emis.de/journals/JIPAM/images/084_05_JIPAM/084_05.pdf">Pi and some other constants</a>, Journal of Inequalities in Pure and Applied Mathematics, Vol. 6, Issue 5, Article 138, 2005.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PiFormulas.html">Pi Formulas</a>
%F Pi = 3*sqrt(3)/4 + 24*(1/12 - sum(n >= 2, (2*n-2)!/((n-1)!^2*(2*n-3)*(2*n+1)*2^(4*n-2)))) (Newton).
%e Pi = 3*sqrt(3)/4 + 24*(0/(1*2) + 2/(3*2^3) - 1/(5*2^5) - 1/(28*2^7) - 1/(72*2^9) - ...)
%Y Cf. A054388.
%K sign
%O 0,2
%A _Eric W. Weisstein_