A210277 a(n) = (3*n)!/3^n.
1, 2, 80, 13440, 5913600, 5381376000, 8782405632000, 23361198981120000, 94566133475573760000, 553211880832106496000000, 4492080472356704747520000000, 49017582114356362204938240000000, 699971072593008852286518067200000000
Offset: 0
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
Programs
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Magma
[Factorial(3*n)/3^n: n in [0..15]]; // Vincenzo Librandi, Feb 15 2013
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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)