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 A090598 Numerator of ((integral_{x = 0..1/2} 1/(1+x^2)^(n + 1/2) dx) * sqrt(1/5)). 0

%I

%S 1,14,328,10800,458880,23911680,1477278720,105623562240,8582728089600,

%T 781478859571200,78834419151667200,8729454895025356800,

%U 1052840115930503577600,137399767923711541248000

%N Numerator of ((integral_{x = 0..1/2} 1/(1+x^2)^(n + 1/2) dx) * sqrt(1/5)).

%C Denominator is b(n)=5^(n-1)*(2*n)!/(n!*2^n). E.g., b(3)=375.

%e a(3) = 328 since f(n) = 328/375.

%t f[n_] := (5^(n - 1/2)(2n - 1)!!Integrate[1/(1 + x^2)^(n + 1/2), {x, 0, 1/2}]); Table[ f[n], {n, 1, 15}] (* _Robert G. Wilson v_, Feb 27 2004 *)

%K nonn,frac

%O 1,2

%A Al Hakanson (hawkuu(AT)excite.com), Feb 25 2004

%E Edited and extended by _Robert G. Wilson v_, Feb 27 2004

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Last modified August 12 16:32 EDT 2022. Contains 356077 sequences. (Running on oeis4.)