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Search: id:A122217
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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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+0
6
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| 1, 1, 3, 27, 3645, 184528125, 3065257232666015625, 25071642180724968784488737583160400390625, 80220075338110866905430754850505863041381217435482620103925910370890051126480102\ 5390625
(list; graph; listen)
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OFFSET
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0,3
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REFERENCES
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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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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
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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 (noe(AT)sspectra.com), Nov 16 2006
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CROSSREFS
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Cf. A092799. Numerators are A122216. Reduced denominators are A122215.
Sequence in context: A009039 A137092 A122215 this_sequence A068221 A068222 A055777
Adjacent sequences: A122214 A122215 A122216 this_sequence 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 (jsondow(AT)alumni.princeton.edu), Aug 26 2006
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EXTENSIONS
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Corrected by T. D. Noe (noe(AT)sspectra.com), Nov 16 2006
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