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A089252
a(n) = ((2*n-1)!!/sqrt(3))*(integral_{x=0..sqrt(3/4)} 1/(1-x^2)^(n+1/2) dx).
1
1, 6, 72, 1392, 38016, 1347840, 58752000, 3036579840, 181428387840, 12299042488320, 932514044313600, 78184097316864000, 7181946863065497600, 717283471185779097600, 77383645289778040012800
OFFSET
1,2
FORMULA
E.g.f.: (sqrt(3)/3)*arccot(sqrt(3-24*x)/3). a(n+1) = 2^n*n!*A006134(n). - Description corrected by Vladeta Jovovic, Dec 14 2003
D-finite with recurrence: a(n) +2*(-5*n+7)*a(n-1) +8*(2*n-3)*(n-2)*a(n-2)=0. - R. J. Mathar, Jan 24 2020
MATHEMATICA
f[n_] := Simplify[(2n - 1)!!/Sqrt[3]* Integrate[1/(1 - x^2)^(n + 1/2), {x, 0, Sqrt[3/4]}]]; Table[ f[n], {n, 1, 16}] (* Robert G. Wilson v, Feb 27 2004 *)
CROSSREFS
Sequence in context: A003235 A113133 A302355 * A052730 A010796 A038095
KEYWORD
nonn
AUTHOR
Al Hakanson (hawkuu(AT)excite.com), Dec 12 2003
EXTENSIONS
More terms from Robert G. Wilson v, Feb 27 2004
STATUS
approved