Search: id:A092798
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%I A092798
%S A092798 2,16,8192,274877906944,5070602400912917605986812821504,
%T A092798 115792089237316195423570985008687907853269984665640564039457584007913129639936
%N A092798 Numerator of partial products in an approximation of Pi/2.
%D A092798 J. Sondow, A faster product for Pi and a new integral for ln Pi/2, Amer. 
               Math. Monthly 112 (2005) 729-734.
%H A092798 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>
%H A092798 J. Sondow, <a href="http://www.arXiv.org/abs/math.NT/0401406">A faster 
               product for Pi and a new integral for ln(Pi/2)</a>
%F A092798 a(n) = Product_{k=1...n+1} A122214(k)^2^(n-k+1). - Jonathan Sondow (jsondow(AT)alumni.princeton.edu), 
               Sep 13 2006
%F A092798 a(n) = Numerator[Product_{k=1...n+1} (A122216(k)/A122217(k))^2^(n-k+1)]. 
               - Jonathan Sondow (jsondow(AT)alumni.princeton.edu), Sep 13 2006
%e A092798 The first approximations are 2^(1/2),(16/3)^(1/4),(8192/243)^(1/8),
%e A092798 (274877906944/215233605)^(1/16).
%o A092798 (PARI) for(m=1,10,p=1:for(n=1,m,p=p*p*(prod(k=1,ceil(n/2),(2*k)^binomial(n,
               2*k-1))/(prod(k=1,floor(n/2)+1,(2*k-1)^binomial(n,2*k-2))))):print(numerator(p)))
%Y A092798 Denominators are in A092799.
%Y A092798 Cf. A000246, A001900, A001901, A001902.
%Y A092798 Cf. A122214, A122216.
%Y A092798 Sequence in context: A138834 A088321 A061301 this_sequence A068916 A093987 
               A114560
%Y A092798 Adjacent sequences: A092795 A092796 A092797 this_sequence A092799 A092800 
               A092801
%K A092798 nonn,easy,frac
%O A092798 1,1
%A A092798 Ralf Stephan (ralf(AT)ark.in-berlin.de), Mar 05 2004

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