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A122217
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Denominators in infinite products for Pi/2, e and e^gamma (unreduced).
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6
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1, 1, 3, 27, 3645, 184528125, 3065257232666015625, 25071642180724968784488737583160400390625, 802200753381108669054307548505058630413812174354826201039259103708900511264801025390625
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OFFSET
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0,3
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REFERENCES
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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.
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LINKS
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Table of n, a(n) for n=0..8.
J. Baez, This Week's Finds in Mathematical Physics
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.
J. Sondow, A faster product for Pi and a new integral for ln Pi/2
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FORMULA
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a(n) = product(k = 1...floor(n/2)+1, (2k-1)^binomial(n,2k-2)).
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EXAMPLE
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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) *
...
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MATHEMATICA
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Table[Product[(2k-1)^Binomial[n, 2k-2], {k, 1+Floor[n/2]}], {n, 0, 8}] - T. D. Noe, Nov 16 2006
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CROSSREFS
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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
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KEYWORD
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frac,nonn
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AUTHOR
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Jonathan Sondow, Aug 26 2006
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EXTENSIONS
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Corrected by T. D. Noe, Nov 16 2006
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STATUS
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approved
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