A228484 - OEIS

%I #26 Jul 25 2024 08:46:03

%S 1,6,60,672,7920,96096,1188096,14883840,188280576,2399654400,

%T 30766095360,396363202560,5126871859200,66538909237248,

%U 866061993246720,11300615801536512,147773778404769792,1936073567335219200,25408660721789829120,333963051307735449600

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

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

%H Vincenzo Librandi, <a href="/A228484/b228484.txt">Table of n, a(n) for n = 0..200</a>

%F a(n) = 2^n*A005809(n).

%F a(n) = A013609(3*n, n).

%F a(n) = A006588(n)/2^n.

%F a(n) = (2*n+1)*A153231(n).

%F Asymptotic approximation of a(n) ~ C*(13.5)^n/sqrt(n) with C = (1/2)*sqrt(3/Pi) = A137209.

%F Sum_{n>=0} 1/a(n) = (11*Pi - 12*log(2) + 270)/250. - _Amiram Eldar_, Mar 06 2022

%p a := n -> 2^n*binomial(3*n, n): seq(a(n), n=0..16);

%t Table[2^n (3 n)!/(n! (2 n)!), {n, 0, 20}] (* _Vincenzo Librandi_, Aug 24 2013 *)

%o (Magma) [2^n*Factorial(3*n)/(Factorial(n)*Factorial(2*n)): n in [0..20]]; // _Vincenzo Librandi_, Aug 24 2013

%o (PARI) a(n) = 2^n*binomial(3*n, 2*n); \\ _Michel Marcus_, Mar 06 2022

%Y Cf. A005809, A013609, A006588, A137209.

%K nonn,easy

%O 0,2

%A _Johannes W. Meijer_, Aug 22 2013

%E More terms from _Vincenzo Librandi_, Aug 24 2013