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%I #40 Dec 11 2017 06:29:42
%S 1,1,3,9,45,75,175,1225,11025,19845,43659,160083,693693,1288287,
%T 2760615,41409225,703956825,1329696225,2807136475,10667118605,
%U 44801898141,85530896451,178837328943,1371086188563,11425718238025
%N Successive denominators of Wallis's approximation to Pi/2 (reduced).
%D H.-D. Ebbinghaus et al., Numbers, Springer, 1990, p. 146.
%H J. Sondow, <a href="https://arxiv.org/abs/math/0401406">A faster product for Pi and a new integral for ln(Pi/2)</a>, arXiv:math/0401406 [math.NT], 2004.
%H J. Sondow, <a href="http://www.jstor.org/stable/30037575">A faster product for Pi and a new integral for ln(Pi/2)</a>, Amer. Math. Monthly 112 (2005), 729-734 and 113 (2006), 670.
%F (2*2*4*4*6*6*8*8*...*2n*2n*...)/(1*3*3*5*5*7*7*9*...*(2n-1)*(2n+1)*...) for n >= 1.
%F From _Wolfdieter Lang_, Dec 07 2017: (Start)
%F 1/1 * 2/1 * 2/3 * 4/3 * 4/5 * 6/5 * 6/7 * ...; partial products (reduced). Here the denominators with offset 0.
%F a(n) = denominator(W(n)), for n >= 0, with W(n) = Product_{k=0..n} N(k)/D(k) (reduced), with N(k) = 2*floor((k+1)/2) for k >= 1 and N(0) = 1, and D(k) = 2*floor(k/2) + 1, for k >= 0. (End)
%e From _Wolfdieter Lang_, Dec 07 2017: (Start)
%e See the table in A001901 for details.
%e n = 5: numerator(1*2*2*4*4*6/(1*1*3*3*5*5)) = denominator(384/225) = denominator(128/75) = 75. (End)
%t a[n_?EvenQ] := n!!^2/((n - 1)!!^2*(n + 1)); a[n_?OddQ] := (n - 1)!!^2*(n + 1)/n!!^2; Table[a[n] // Denominator, {n, 0, 23}] (* _Jean-François Alcover_, Jun 19 2013 *)
%Y Numerators are A001901. For the unreduced form see A001900(n)/A000246(n+1), n >= 0.
%K nonn,frac,easy
%O 0,3
%A _N. J. A. Sloane_
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