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%I #36 Sep 08 2022 08:46:01
%S 1,2,80,13440,5913600,5381376000,8782405632000,23361198981120000,
%T 94566133475573760000,553211880832106496000000,
%U 4492080472356704747520000000,49017582114356362204938240000000,699971072593008852286518067200000000
%N a(n) = (3*n)!/3^n.
%H Vincenzo Librandi, <a href="/A210277/b210277.txt">Table of n, a(n) for n = 0..100</a>
%H D. Bevan, D. Levin, P. Nugent, J. Pantone and L. Pudwell, <a href="http://arxiv.org/abs/1510.08036">Pattern avoidance in forests of binary shrubs</a>, arXiv preprint arXiv:1510:08036 [math.CO], 2015-2016.
%F E.g.f.: 1/(1-x^3/3).
%F a(n) = Product_{i=1..n} (2*binomial(3i,3)). - _James Mahoney_, Apr 04 2012
%F From _Amiram Eldar_, Jan 18 2021: (Start)
%F Sum_{n>=0} 1/a(n) = exp(3^(1/3))/3 + (2/3)*exp(-3^(1/3)/2)*cos(3^(5/6)/2).
%F 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)
%t Table[(3 n)!/3^n, {n, 0, 15}] (* _Vincenzo Librandi_, Feb 15 2013 *)
%o (Magma)[Factorial(3*n)/3^n: n in [0..15]]; // _Vincenzo Librandi_, Feb 15 2013
%Y Cf. A210278, A000680, A067630, A084939, A084940, A084941, A084942, A084943, A084944, A087127, A001147, A132101.
%K nonn,easy
%O 0,2
%A _Mohammad K. Azarian_, Mar 20 2012
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