A122217 - OEIS

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A122217

Denominators in infinite products for Pi/2, e and e^gamma (unreduced).

1, 1, 3, 27, 3645, 184528125, 3065257232666015625, 25071642180724968784488737583160400390625, 802200753381108669054307548505058630413812174354826201039259103708900511264801025390625

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OFFSET

0,3

LINKS

Table of n, a(n) for n=0..8.

Mohammad K. Azarian, Euler's Number Via Difference Equations, International Journal of Contemporary Mathematical Sciences, Vol. 7, 2012, No. 22, pp. 1095 - 1102.

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; 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..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) *

...