A228484 a(n) = 2^n*(3*n)!/(n!*(2*n)!).

1, 6, 60, 672, 7920, 96096, 1188096, 14883840, 188280576, 2399654400, 30766095360, 396363202560, 5126871859200, 66538909237248, 866061993246720, 11300615801536512, 147773778404769792, 1936073567335219200, 25408660721789829120, 333963051307735449600

Offset: 0

Author

Johannes W. Meijer, Aug 22 2013

Keywords

• nonn
• easy

Comments

Oblique diagonal of the Pell-Jacobsthal triangle A013609. Its mirror diagonal is A006588.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200

Crossrefs

Cf. A005809, A013609, A006588, A137209.

Programs

Magma

[2^n*Factorial(3*n)/(Factorial(n)*Factorial(2*n)): n in [0..20]]; // Vincenzo Librandi, Aug 24 2013

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 *)

PARI

a(n) = 2^n*binomial(3*n, 2*n); \\ Michel Marcus, Mar 06 2022

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

From Karol A. Penson, Feb 26 2025: (Start)

G.f.: hypergeom([1/3,2/3],[1/2],27*z/2).

E.g.f.: hypergeom([1/3,2/3],[1/2,1],27*z/2). (End)

Extensions

More terms from Vincenzo Librandi, Aug 24 2013