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A257589
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a(n) = (2n+1)^2*Catalan(n).
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1
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1, 9, 50, 245, 1134, 5082, 22308, 96525, 413270, 1755182, 7407036, 31097794, 130007500, 541574100, 2249204040, 9316746045, 38504502630, 158814867750, 653887380300, 2688007311990, 11034286426020, 45238127719980, 185252191371000, 757818686552850, 3097059857724924
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OFFSET
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0,2
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LINKS
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FORMULA
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a(n) = (n + 1/2)*(2*n + 2)! / (n + 1)!^2. - Peter Luschny, Feb 15 2023
Sum_{n>=0} 1/a(n) = Pi/(3*sqrt(3)) - log(2+sqrt(3))*Pi/6 + 4*G/3, where G is Catalan's constant (A006752). - Amiram Eldar, Feb 16 2023
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MAPLE
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a := n -> (n + 1/2)*(2*n + 2)!/(n + 1)!^2: seq(a(n), n = 0..22); # Peter Luschny, Feb 15 2023
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MATHEMATICA
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Table[(2n+1)^2 CatalanNumber[n], {n, 0, 30}] (* Harvey P. Dale, Sep 02 2015 *)
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PROG
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(PARI) a(n) = (2*n+1)^2*binomial(2*n, n)/(n+1); \\ Michel Marcus, Jun 11 2019
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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