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Search: id:A092798
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| A092798 |
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Numerator of partial products in an approximation of Pi/2. |
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+0
5
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| 2, 16, 8192, 274877906944, 5070602400912917605986812821504, 115792089237316195423570985008687907853269984665640564039457584007913129639936
(list; graph; listen)
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OFFSET
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1,1
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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. Sondow, A faster product for Pi and a new integral for ln(Pi/2)
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...n+1} A122214(k)^2^(n-k+1). - Jonathan Sondow (jsondow(AT)alumni.princeton.edu), Sep 13 2006
a(n) = Numerator[Product_{k=1...n+1} (A122216(k)/A122217(k))^2^(n-k+1)]. - Jonathan Sondow (jsondow(AT)alumni.princeton.edu), Sep 13 2006
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EXAMPLE
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The first approximations are 2^(1/2),(16/3)^(1/4),(8192/243)^(1/8),
(274877906944/215233605)^(1/16).
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PROGRAM
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(PARI) for(m=1, 10, p=1:for(n=1, m, p=p*p*(prod(k=1, ceil(n/2), (2*k)^binomial(n, 2*k-1))/(prod(k=1, floor(n/2)+1, (2*k-1)^binomial(n, 2*k-2))))):print(numerator(p)))
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CROSSREFS
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Denominators are in A092799.
Cf. A000246, A001900, A001901, A001902.
Cf. A122214, A122216.
Adjacent sequences: A092795 A092796 A092797 this_sequence A092799 A092800 A092801
Sequence in context: A138834 A061301 A088321 this_sequence A068916 A093987 A114560
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KEYWORD
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nonn,easy,frac
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AUTHOR
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Ralf Stephan (ralf(AT)ark.in-berlin.de), Mar 05 2004
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