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A003409
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a(n) = 3*binomial(2n-1,n).
(Formerly M2814)
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8
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3, 9, 30, 105, 378, 1386, 5148, 19305, 72930, 277134, 1058148, 4056234, 15600900, 60174900, 232676280, 901620585, 3500409330, 13612702950, 53017895700, 206769793230, 807386811660, 3156148445580, 12350146091400, 48371405524650, 189615909656628, 743877799422156
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OFFSET
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1,1
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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FORMULA
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a(n) = (3/2)*4^n*Gamma(1/2+n)/(sqrt(Pi)*Gamma(1+n)). - Peter Luschny, Dec 14 2015
O.g.f.: 6*x/((1 - sqrt(1 - 4*x))*sqrt(1 - 4*x)) - 3.
E.g.f.: 3*(exp(2*x)*I_0(2*x) - 1)/2, where I_n(x) is the modified Bessel function of the first kind.
a(n) ~ 3*4^n/(2*sqrt(n*Pi)). (End)
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MAPLE
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a := n -> (3/2)*4^n*GAMMA(1/2+n)/(sqrt(Pi)*GAMMA(1+n)):
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MATHEMATICA
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Table[3*Binomial[2*n - 1, n], {n, 20}] (* T. D. Noe, Oct 07 2013 *)
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PROG
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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