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A228484
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a(n) = 2^n*(3*n)!/(n!*(2*n)!).
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2
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1, 6, 60, 672, 7920, 96096, 1188096, 14883840, 188280576, 2399654400, 30766095360, 396363202560, 5126871859200, 66538909237248, 866061993246720, 11300615801536512, 147773778404769792, 1936073567335219200, 25408660721789829120, 333963051307735449600
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OFFSET
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0,2
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COMMENTS
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Oblique diagonal of the Pell-Jacobsthal triangle A013609. Its mirror diagonal is A006588.
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LINKS
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FORMULA
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Asymptotic approximation of a(n) ~ C*(13.5)^n/sqrt(n) with C = (1/2)*sqrt(3/Pi) = A137209.
Sum_{n>=0} 1/a(n) = (11*Pi - 12*log(2) + 270)/250. - Amiram Eldar, Mar 06 2022
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MAPLE
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a := n -> 2^n*binomial(3*n, n): seq(a(n), n=0..16);
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MATHEMATICA
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PROG
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(Magma) [2^n*Factorial(3*n)/(Factorial(n)*Factorial(2*n)): n in [0..20]]; // Vincenzo Librandi, Aug 24 2013
(PARI) a(n) = 2^n*binomial(3*n, 2*n); \\ Michel Marcus, Mar 06 2022
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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