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%I #12 Feb 05 2021 00:26:08
%S 1,35,2271,218793,28137345,4539496635,882318678255,200816025228945,
%T 52409174427470385,15432871959522241875,5062570863876165491775,
%U 1830983671801954093988025,723885864573750477727953825
%N Numerator of I(n) = Integral_{x=1..9/8} (sqrt(x^2-1)/x)^(2*n) dx.
%C The denominator is b(n) = 8*9^(2*n-1)*(2*n)!/(n!*2^n).
%F 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
%e I(3) = 2271/7085880. b(3) = 7085880.
%p A094187 := proc(n)
%p ((x^2-1)/x^2)^n ;
%p int(%,x=1..9/8) ;
%p %*8*9^(2*n-1)*(2*n)!/(n!*2^n) ;
%p end proc:
%p seq(A094187(n),n=1..30) ; # _R. J. Mathar_, Feb 04 2021
%t 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 *)
%K nonn,frac
%O 1,2
%A Al Hakanson (hawkuu(AT)excite.com), May 24 2004
%E Edited and extended by _Robert G. Wilson v_, May 29 2004
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