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A094187
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Numerator of I(n) = Integral_{x=1..9/8} (sqrt(x^2-1)/x)^(2*n) dx.
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1
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1, 35, 2271, 218793, 28137345, 4539496635, 882318678255, 200816025228945, 52409174427470385, 15432871959522241875, 5062570863876165491775, 1830983671801954093988025, 723885864573750477727953825
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OFFSET
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1,2
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COMMENTS
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The denominator is b(n) = 8*9^(2*n-1)*(2*n)!/(n!*2^n).
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LINKS
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FORMULA
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Conjecture D-finite with recurrence a(n) + (-196*n+51)*a(n-1) + 2754*(n-1)*(2*n-3)*a(n-2) = 0. - R. J. Mathar, Feb 04 2021
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EXAMPLE
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I(3) = 2271/7085880. b(3) = 7085880.
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MAPLE
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((x^2-1)/x^2)^n ;
int(%, x=1..9/8) ;
%*8*9^(2*n-1)*(2*n)!/(n!*2^n) ;
end proc:
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MATHEMATICA
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a[n_] := (8*9^(2*n - 1)*(2*n)!/(n!*2^n))Integrate[(Sqrt[(x^2 - 1)]/x)^(2n), {x, 1, 9/8}]; Table[ a[n], {n, 13}] (* Robert G. Wilson v, May 29 2004 *)
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CROSSREFS
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KEYWORD
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nonn,frac
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AUTHOR
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Al Hakanson (hawkuu(AT)excite.com), May 24 2004
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EXTENSIONS
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STATUS
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approved
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