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Search: id:A056982
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| 1, 4, 64, 256, 16384, 65536, 1048576, 4194304, 1073741824, 4294967296, 68719476736, 274877906944, 17592186044416, 70368744177664, 1125899906842624, 4503599627370496, 4611686018427387904
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Also equal to A046161(n)^2.
Let W(n)=Prod(k=1,n,1-1/4/k^2), the partial Wallis product with lim n -> infinity W(n)=2/Pi; a(n)=denominator(W(n)).
Equivalently, denominators in partial products of the following approximation to Pi: Pi = Product_{n >= 1} 4*n^2/(4*n^2-1). Numerators are in A069955.
Denominator of h^(2n) in the Kummer-Gauss series for the perimeter of an ellipse.
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REFERENCES
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O. J. Farrell and B. Ross, Solved Problems in Analysis, Dover, NY, 1971; p. 77.
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LINKS
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B. Gourevitch, L'univers de Pi
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics (1).
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics (2).
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CROSSREFS
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Apart from offset, identical to A110258.
Cf. A005187, A046161, A056981.
Equals (1/2)*A038533(n).
Sequence in context: A016934 A056229 A062271 this_sequence A110258 A030994 A064935
Adjacent sequences: A056979 A056980 A056981 this_sequence A056983 A056984 A056985
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KEYWORD
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nonn,frac
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AUTHOR
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Eric Weisstein (eric(AT)weisstein.com)
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EXTENSIONS
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Edited by njas, Feb 18 2004, Jun 05 2007
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