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A095839
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Numerator of I(n)=integral_{x=1/2..1} (Sqrt(1-x^2)/x)^(2*n) dx.
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0
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1, 1, 5, 51, 807, 17445, 479565, 16019955, 630301455, 28552506885, 1463744449125, 83780913568275
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| The denominator is b(n)=(2*n)!/(n!*2^(n-1).
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MATHEMATICA
| f[n_] := Numerator[ Integrate[(Sqrt[1 - x^2]/x)^(2n), {x, 1/2, 1}]*(2n)!/(n!2^(n + 1)!)]; Table[ f[n], {n, 0, 11}] (* Robert G. Wilson v *)
Numerator[2^(-2 - Gamma[2 + n])*3^(1 + n)*(2*n)!* Hypergeometric2F1Regularized[1, 1/2 + n, 2 + n, -3]] Eric Weisstein (eww(AT)wolfram.com), Nov 19 2005.
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CROSSREFS
| Sequence in context: A154886 A145162 A187235 * A107669 A077392 A193444
Adjacent sequences: A095836 A095837 A095838 * A095840 A095841 A095842
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KEYWORD
| nonn
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AUTHOR
| Al Hakanson (Hawkuu(AT)excite.com), Jun 08 2004
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EXTENSIONS
| a(8)-a(11) from Robert G. Wilson v (rgwv(at)rgwv.com), Nov 18 2005
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