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 A092799 Denominator of partial products in an approximation to Pi/2. 3
 1, 3, 243, 215233605, 2849452841966467687734375, 34139907905802495953388390516678108673704867996275424957275390625 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS J. Guillera and J. Sondow, Double integrals and infinite products for some classical constants via analytic continuations of Lerch's transcendent, Ramanujan J. 16 (2008) 247-270; arXiv:math/0506319 [math.NT], 2005-2006. J. Sondow, A faster product for Pi and a new integral for ln(Pi/2), arXiv:math/0401406 [math.NT], 2004. J. Sondow, A faster product for Pi and a new integral for ln(Pi/2), Amer. Math. Monthly 112 (2005), 729-734 and 113 (2006), 670. FORMULA a(n) = Product_{k=1..n+1} A122215(k)^2^(n-k+1). - Jonathan Sondow, Sep 13 2006 a(n) = Denominator(Product_{k=1..n+1} (A122216(k)/A122217(k))^2^(n-k+1)). - Jonathan Sondow, Sep 13 2006 EXAMPLE The first approximations are 2^(1/2), (16/3)^(1/4), (8192/243)^(1/8), (274877906944/215233605)^(1/16). PROG (PARI) for(m=1, 7, 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))))); print1(denominator(p), ", ")) CROSSREFS Numerators are in A092798. Cf. A000246, A001900, A001901, A001902. Cf. A122215, A122217. Sequence in context: A338453 A013778 A146313 * A229690 A140163 A157573 Adjacent sequences:  A092796 A092797 A092798 * A092800 A092801 A092802 KEYWORD nonn,easy,frac AUTHOR Ralf Stephan, Mar 05 2004 STATUS approved

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Last modified September 27 19:34 EDT 2021. Contains 347694 sequences. (Running on oeis4.)