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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

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

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 * 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

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Last modified October 18 22:40 EDT 2018. Contains 316327 sequences. (Running on oeis4.)