A210277 a(n) = (3*n)!/3^n.

1, 2, 80, 13440, 5913600, 5381376000, 8782405632000, 23361198981120000, 94566133475573760000, 553211880832106496000000, 4492080472356704747520000000, 49017582114356362204938240000000, 699971072593008852286518067200000000

Offset: 0

Author

Mohammad K. Azarian, Mar 20 2012

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..100
• D. Bevan, D. Levin, P. Nugent, J. Pantone and L. Pudwell, Pattern avoidance in forests of binary shrubs, arXiv preprint arXiv:1510:08036 [math.CO], 2015-2016.

Crossrefs

Cf. A210278, A000680, A067630, A084939, A084940, A084941, A084942, A084943, A084944, A087127, A001147, A132101.

Programs

Magma

[Factorial(3*n)/3^n: n in [0..15]]; // Vincenzo Librandi, Feb 15 2013

Mathematica

Table[(3 n)!/3^n, {n, 0, 15}] (* Vincenzo Librandi, Feb 15 2013 *)

Formula

E.g.f.: 1/(1-x^3/3).

a(n) = Product_{i=1..n} (2*binomial(3i,3)). - James Mahoney, Apr 04 2012

From Amiram Eldar, Jan 18 2021: (Start)

Sum_{n>=0} 1/a(n) = exp(3^(1/3))/3 + (2/3)*exp(-3^(1/3)/2)*cos(3^(5/6)/2).

Sum_{n>=0} (-1)^n/a(n) = exp(-3^(1/3))/3 + (2/3)*exp(3^(1/3)/2)*cos(3^(5/6)/2). (End)