Search: id:A157142
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%I A157142
%S A157142 1,3,5,7,9,11,13,15,17,19,21,23,25,27,29,31,33,35,37,39,41,
%T A157142 43,45,47,49,51,53,55,57,59,61,63,65,67,69,71,73,75,77,79,81,
%U A157142 83,85,87,89,91,93,95,97,99,101,103,105,107,109,111,113,115
%V A157142 1,-3,5,-7,9,-11,13,-15,17,-19,21,-23,25,-27,29,-31,33,-35,37,-39,41,
%W A157142 -43,45,-47,49,-51,53,-55,57,-59,61,-63,65,-67,69,-71,73,-75,77,-79,81,
%X A157142 -83,85,-87,89,-91,93,-95,97,-99,101,-103,105,-107,109,-111,113,-115
%N A157142 Denominators of Leibniz series for Pi/4
%C A157142 Numerators are all 1.
%C A157142 Sum_{n=0..inf}1/a(n)=Pi/4
%H A157142 X. Gourdon and P. Sebah, <a href="http://numbers.computation.free.fr/
               Constants/Pi/pi.html">Archimedes' constant</a>
%H A157142 Mathpages, <a href="http://www.mathpages.com/home/kmath477.htm">How Leibniz 
               might have anticipated Euler</a>
%H A157142 Wikipedia, <a href="http://en.wikipedia.org/wiki/Leibniz_formula_for_pi">
               Leibniz formula for Pi</a>
%F A157142 G.f.:(1-x)/(1+x)^2
%F A157142 a(0)=1, a(1)=-3, a(n)=-2a(n-1)-a(n-2) for n>=2
%o A157142 (PARI) a(n)=(2*n+1)*(-1)^n
%Y A157142 a(n)=A005408(n)*A033999(n).
%Y A157142 Cf. A157327. [From Jaume Oliver Lafont (joliverlafont(AT)gmail.com), 
               Mar 03 2009]
%Y A157142 Sequence in context: A081874 A165747 A053229 this_sequence A004273 A005408 
               A144396
%Y A157142 Adjacent sequences: A157139 A157140 A157141 this_sequence A157143 A157144 
               A157145
%K A157142 frac,sign
%O A157142 0,2
%A A157142 Jaume Oliver Lafont (joliverlafont(AT)gmail.com), Feb 24 2009

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