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 A094187 Numerator of I(n) = Integral_{x=1..9/8} (sqrt(x^2-1)/x)^(2*n) dx. 1
 1, 35, 2271, 218793, 28137345, 4539496635, 882318678255, 200816025228945, 52409174427470385, 15432871959522241875, 5062570863876165491775, 1830983671801954093988025, 723885864573750477727953825 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The denominator is b(n) = 8*9^(2*n-1)*(2*n)!/(n!*2^n). LINKS FORMULA 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 EXAMPLE I(3) = 2271/7085880. b(3) = 7085880. MAPLE A094187 := proc(n)     ((x^2-1)/x^2)^n ;     int(%, x=1..9/8) ;     %*8*9^(2*n-1)*(2*n)!/(n!*2^n) ; end proc: seq(A094187(n), n=1..30) ; # R. J. Mathar, Feb 04 2021 MATHEMATICA 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 *) CROSSREFS Sequence in context: A183417 A199587 A001825 * A202921 A215291 A249886 Adjacent sequences:  A094184 A094185 A094186 * A094188 A094189 A094190 KEYWORD nonn,frac AUTHOR Al Hakanson (hawkuu(AT)excite.com), May 24 2004 EXTENSIONS Edited and extended by Robert G. Wilson v, May 29 2004 STATUS approved

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Last modified January 24 21:35 EST 2022. Contains 350565 sequences. (Running on oeis4.)