A094187 - OEIS

A094187

Numerator of I(n) = Integral_{x=1..9/8} (sqrt(x^2-1)/x)^(2*n) dx.

1, 35, 2271, 218793, 28137345, 4539496635, 882318678255, 200816025228945, 52409174427470385, 15432871959522241875, 5062570863876165491775, 1830983671801954093988025, 723885864573750477727953825

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OFFSET

1,2

COMMENTS

The denominator is b(n) = 8*9^(2*n-1)*(2*n)!/(n!*2^n).

LINKS

Table of n, a(n) for n=1..13.

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