cp's OEIS Frontend

A122217 Denominators in infinite products for Pi/2, e and e^gamma (unreduced).

%I A122217 #21 Jun 03 2019 08:00:34
%S A122217 1,1,3,27,3645,184528125,3065257232666015625,
%T A122217 25071642180724968784488737583160400390625,
%U A122217 802200753381108669054307548505058630413812174354826201039259103708900511264801025390625
%N A122217 Denominators in infinite products for Pi/2, e and e^gamma (unreduced).
%H A122217 Mohammad K. Azarian, <a href="http://www.m-hikari.com/ijcms/ijcms-2012/21-24-2012/azarianIJCMS21-24-2012.pdf">Euler's Number Via Difference Equations</a>, International Journal of Contemporary Mathematical Sciences, Vol. 7, 2012, No. 22, pp. 1095 - 1102.
%H A122217 J. Baez, <a href="http://math.ucr.edu/home/baez/week230.html">This Week's Finds in Mathematical Physics</a>
%H A122217 J. Guillera and J. Sondow, <a href="https://arxiv.org/abs/math/0506319">Double integrals and infinite products for some classical constants via analytic continuations of Lerch's transcendent</a>, Ramanujan J. 16 (2008) 247-270; arXiv:math/0506319 [math.NT], 2005-2006.
%H A122217 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 A122217 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 A122217 a(n) = Product_{k=1..floor(n/2)+1} (2k-1)^binomial(n,2k-2).
%e A122217 Pi/2 = (2/1)^(1/2) * (4/3)^(1/4) * (32/27)^(1/8) *
%e A122217 (4096/3645)^(1/16) * ...,
%e A122217 e = (2/1)^(1/1) * (4/3)^(1/2) * (32/27)^(1/3) * (4096/3645)^(1/4) * ... and
%e A122217 e^gamma = (2/1)^(1/2) * (4/3)^(1/3) * (32/27)^(1/4) * (4096/3645)^(1/5) *
%e A122217 ...
%t A122217 Table[Product[(2k-1)^Binomial[n,2k-2], {k,1+Floor[n/2]}], {n,0,8}] (* _T. D. Noe_, Nov 16 2006 *)
%Y A122217 Cf. A092799. Numerators are A122216. Reduced denominators are A122215.
%K A122217 frac,nonn
%O A122217 0,3
%A A122217 _Jonathan Sondow_, Aug 26 2006
%E A122217 Corrected by _T. D. Noe_, Nov 16 2006