%I A122214
%S A122214 1,2,4,32,4096,67108864,4503599627370496,
%T A122214 2535301200456458802993406410752,
%U A122214 4084620902943761579745625423246687265522976897405582347410338578593480704
%N A122214 Numerators in infinite products for Pi/2, e and e^gamma (reduced).
%D A122214 J. Sondow, A faster product for Pi and a new integral for ln Pi/2, Amer. 
               Math. Monthly 112 (2005) 729-734.
%H A122214 J. Baez, <a href="http://math.ucr.edu/home/baez/week230.html">This Week's 
               Finds in Mathematical Physics</a>
%H A122214 J. Guillera and J. Sondow, <a href="http://arXiv.org/abs/math.NT/0506319">
               Double integrals and infinite products for some classical constants 
               via analytic continuations of Lerch's transcendent</a>
%F A122214 a(n) = numerator(product(k = 1...n, k^((-1)^k*binomial(n-1,k-1)))).
%e A122214 Pi/2 = (2/1)^(1/2) * (4/3)^(1/4) * (32/27)^(1/8) * (4096/3645)^(1/16) 
               * ...,
%e A122214 e = (2/1)^(1/1) * (4/3)^(1/2) * (32/27)^(1/3) * (4096/3645)^(1/4) * ... 
               and
%e A122214 e^gamma = (2/1)^(1/2) * (4/3)^(1/3) * (32/27)^(1/4) * (4096/3645)^(1/
               5) * ....
%Y A122214 Cf. A092798. Denominators are A122215. Unreduced numerators are A122216.
%Y A122214 Sequence in context: A101460 A118992 A062740 this_sequence A122216 A100117 
               A073888
%Y A122214 Adjacent sequences: A122211 A122212 A122213 this_sequence A122215 A122216 
               A122217
%K A122214 frac,nonn
%O A122214 1,2
%A A122214 Jonathan Sondow (jsondow(AT)alumni.princeton.edu), Aug 26 2006