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A228484
a(n) = 2^n*(3*n)!/(n!*(2*n)!).
2
1, 6, 60, 672, 7920, 96096, 1188096, 14883840, 188280576, 2399654400, 30766095360, 396363202560, 5126871859200, 66538909237248, 866061993246720, 11300615801536512, 147773778404769792, 1936073567335219200, 25408660721789829120, 333963051307735449600
OFFSET
0,2
COMMENTS
Oblique diagonal of the Pell-Jacobsthal triangle A013609. Its mirror diagonal is A006588.
LINKS
FORMULA
a(n) = 2^n*A005809(n).
a(n) = A013609(3*n, n).
a(n) = A006588(n)/2^n.
a(n) = (2*n+1)*A153231(n).
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
MAPLE
a := n -> 2^n*binomial(3*n, n): seq(a(n), n=0..16);
MATHEMATICA
Table[2^n (3 n)!/(n! (2 n)!), {n, 0, 20}] (* Vincenzo Librandi, Aug 24 2013 *)
PROG
(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
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Johannes W. Meijer, Aug 22 2013
EXTENSIONS
More terms from Vincenzo Librandi, Aug 24 2013
STATUS
approved