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A091814
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Numerator of I(n) = (integral_{x=0..1/2}(1-x^2)^n,dx), where the denominator is b(n) = 2^n*(2*n+2)!/(n+1)!.
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1
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1, 11, 203, 5277, 177369, 7324395, 359148915, 20407879485, 1319403598065, 95675323922955, 7692687010986075, 679392106087204125, 65389701973681233225, 6813133489461071047275, 764091914039696003436675
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OFFSET
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0,2
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COMMENTS
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Also numerator of a(n)=(integral_{x=0 to 1}(4-x^2)^n dx)m where the denominator is b(n)=(2*n+2)!/((n+1)!*2^(n+1)). E.g., a(3)=5277/105. b(3)=105.
Also numerator of I(n)=(integral_{x=0 to 1}(4-x^2)^n dx) where the denominator is b(n)=(2*n+2)!/((n+1)!*2^(n+1)). E.g. I(3)=5277/105. b(3)=105. - Robert G. Wilson v, Mar 15 2004
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LINKS
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FORMULA
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a(n) = 2^(n-1)*((2n)!/n!)*J(n) where J(n) = integral( t=0, Pi/6, cos(t)^(2n-1) dt) is given by the order-2 recursion: J(1)=1/2, J(2)=11/24, J(n) = 1/(8*n-4)*((14*n-17)*J(n-1) - 6*(n-2)*J(n-1)). - Benoit Cloitre, Sep 30 2006
Asymptotics: a(n) ~ 2^(n-2)*((2n)!/n!)*sqrt(Pi/n). - Sascha Kurz, Feb 02 2012
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EXAMPLE
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I(3)=5277/13440, a(3) = 5277, b(3)=13440.
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MATHEMATICA
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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Al Hakanson (hawkuu(AT)excite.com), Mar 07 2004
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EXTENSIONS
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STATUS
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approved
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