

A122217


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


6



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) 247270; arXiv:math/0506319 [math.NT], 20052006.
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), 729734 and 113 (2006), 670.


FORMULA

a(n) = Product_{k=1..floor(n/2)+1} (2k1)^binomial(n,2k2).


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[(2k1)^Binomial[n, 2k2], {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: A009039 A137092 A122215 * A316368 A068221 A068222
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



