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%I #13 Jan 30 2020 21:29:15
%S 1,6,72,1392,38016,1347840,58752000,3036579840,181428387840,
%T 12299042488320,932514044313600,78184097316864000,7181946863065497600,
%U 717283471185779097600,77383645289778040012800
%N a(n) = ((2*n-1)!!/sqrt(3))*(integral_{x=0..sqrt(3/4)} 1/(1-x^2)^(n+1/2) dx).
%F 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
%F 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
%t 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 *)
%K nonn
%O 1,2
%A Al Hakanson (hawkuu(AT)excite.com), Dec 12 2003
%E More terms from _Robert G. Wilson v_, Feb 27 2004
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