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 A122217 Denominators in infinite products for Pi/2, e and e^gamma (unreduced). 6
 1, 1, 3, 27, 3645, 184528125, 3065257232666015625, 25071642180724968784488737583160400390625, 802200753381108669054307548505058630413812174354826201039259103708900511264801025390625 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 REFERENCES Mohammad K. Azarian, Euler's Number Via Difference Equations, International Journal of Contemporary Mathematical Sciences, Vol. 7, 2012, No. 22, pp. 1095 - 1102. J. Sondow, A faster product for Pi and a new integral for ln Pi/2, Amer. Math. Monthly 112 (2005) 729-734. 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. FORMULA a(n) = product(k = 1...floor(n/2)+1, (2k-1)^binomial(n,2k-2)). EXAMPLE Pi/2 = (2/1)^(1/2) * (4/3)^(1/4) * (32/27)^(1/8) * (4096/3645)^(1/16) * ..., e = (2/1)^(1/1) * (4/3)^(1/2) * (32/27)^(1/3) * (4096/3645)^(1/4) * ... and e^gamma = (2/1)^(1/2) * (4/3)^(1/3) * (32/27)^(1/4) * (4096/3645)^(1/5) * ... MATHEMATICA Table[Product[(2k-1)^Binomial[n, 2k-2], {k, 1+Floor[n/2]}], {n, 0, 8}] - T. D. Noe, Nov 16 2006 CROSSREFS Cf. A092799. Numerators are A122216. Reduced denominators are A122215. Sequence in context: A137092 A170921 A122215 * A068221 A068222 A055777 Adjacent sequences:  A122214 A122215 A122216 * A122218 A122219 A122220 KEYWORD frac,nonn AUTHOR Jonathan Sondow, Aug 26 2006 EXTENSIONS Corrected by T. D. Noe, Nov 16 2006 STATUS approved

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