%I A007509 M2061
%S A007509 1,2,13,76,263,2578,36979,33976,622637,11064338,11757173,255865444,
%T A007509 1346255081,3852854518,116752370597,3473755390832,3610501179557,
%U A007509 3481569435902,133330680156299,129049485078524,5457995496252709
%N A007509 Numerator of Sum_{k=0..n} (-1)^k/(2*k+1).
%C A007509 Denominators of convergents to 4/pi.
%D A007509 P. Beckmann, A History of Pi. Golem Press, Boulder, CO, 2nd ed., 1971, 
               p. 131.
%D A007509 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%H A007509 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               Pi.html">Link to a section of The World of Mathematics.</a>
%H A007509 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               PiContinuedFraction.html">Link to a section of The World of Mathematics.</
               a>
%e A007509 [ 1 ], 2/3, 13/15, 76/105, 263/315, 2578/3465, 36979/45045, 33976/45045, 
               622637/765765,...
%p A007509 A007509 := n->numer(add((-1)^k/(2*k+1),k=0..n));
%Y A007509 Denominators are A025547.
%Y A007509 Contribution from Johannes W. Meijer (meijgia(AT)hotmail.com), Nov 12 
               2009: (Start)
%Y A007509 Cf. A157142 and A166107.
%Y A007509 Appears in A167576, A167577, A167578, A024199, A167588 and A167589.
%Y A007509 (End)
%Y A007509 Sequence in context: A004027 A154357 A161130 this_sequence A077413 A024199 
               A037523
%Y A007509 Adjacent sequences: A007506 A007507 A007508 this_sequence A007510 A007511 
               A007512
%K A007509 nonn,easy,nice,frac
%O A007509 0,2
%A A007509 N. J. A. Sloane (njas(AT)research.att.com).