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1, 4, 64, 256, 16384, 65536, 1048576, 4194304, 1073741824, 4294967296, 68719476736, 274877906944, 17592186044416, 70368744177664, 1125899906842624, 4503599627370496, 4611686018427387904
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OFFSET
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0,2
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COMMENTS
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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.
Denominators of hypergeometric([1/2,-1/2],[1],x). The numerators are given in A038535. hypergeom([1/2,-1/2],[1],e^2) = L/(2*Pi*a) with the perimeter L of an ellipse with major axis a and numerical eccentricity e (Maclaurin 1742). - Wolfdieter Lang, Nov 08 2010
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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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Charles R Greathouse IV, Table of n, a(n) for n = 0..500
B. Gourevitch, L'univers de Pi
Eric Weisstein's World of Mathematics, Gauss-Kummer Series
Eric Weisstein's World of Mathematics, Ellipse
Index to divisibility sequences
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PROG
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(PARI) a(n)=my(s=n); while(n>>=1, s+=n); 4^s \\ Charles R Greathouse IV, Apr 07 2012
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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: A056229 A062271 * A110258 A030994 A141046 A222557
Adjacent sequences: A056979 A056980 A056981 * A056983 A056984 A056985
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KEYWORD
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nonn,frac,changed
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AUTHOR
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Eric W. Weisstein
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EXTENSIONS
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Edited by N. J. A. Sloane, Feb 18 2004, Jun 05 2007
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STATUS
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approved
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