|
Search: id:A095839
|
|
|
| A095839 |
|
Numerator of I(n)=integral_{x=1/2..1} (Sqrt(1-x^2)/x)^(2*n) dx. |
|
+0
1
|
|
| 1, 1, 5, 51, 807, 17445, 479565, 16019955, 630301455, 28552506885, 1463744449125, 83780913568275
(list; graph; listen)
|
|
|
OFFSET
|
0,3
|
|
|
COMMENT
|
The denominator is b(n)=(2*n)!/(n!*2^(n-1).
|
|
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.
|
|
CROSSREFS
|
Sequence in context: A041040 A154886 A145162 this_sequence A107669 A077392 A111340
Adjacent sequences: A095836 A095837 A095838 this_sequence A095840 A095841 A095842
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Al Hakanson (Hawkuu(AT)excite.com), Jun 08 2004
|
|
EXTENSIONS
|
a(8)-a(11) from Robert G. Wilson v (rgwv(at)rgwv.com), Nov 18 2005
|
|
|
Search completed in 0.002 seconds
|
