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A122216 Numerators in infinite products for Pi/2, e and e^gamma (unreduced). 6
1, 2, 4, 32, 4096, 201326592, 3283124128353091584, 26520146032764463901929624736590416838656, 8409872218845584878346591802015832570333859884111674529900728420499238460920 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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=1..9.

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...ceiling(n/2), (2k)^binomial(n,2k-1)).

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) *

....

CROSSREFS

Cf. A092798. Denominators are A122217. Reduced numerators are A122214.

Sequence in context: A012509 A062740 A122214 * A100117 A073888 A114642

Adjacent sequences:  A122213 A122214 A122215 * A122217 A122218 A122219

KEYWORD

frac,nonn

AUTHOR

Jonathan Sondow, Aug 26 2006

STATUS

approved

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Last modified October 21 06:25 EDT 2018. Contains 316405 sequences. (Running on oeis4.)