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 A210277 a(n) = (3*n)!/3^n. 5
 1, 2, 80, 13440, 5913600, 5381376000, 8782405632000, 23361198981120000, 94566133475573760000, 553211880832106496000000, 4492080472356704747520000000, 49017582114356362204938240000000, 699971072593008852286518067200000000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 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. 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) MATHEMATICA Table[(3 n)!/3^n, {n, 0, 15}] (* Vincenzo Librandi, Feb 15 2013 *) PROG (Magma)[Factorial(3*n)/3^n: n in [0..15]]; // Vincenzo Librandi, Feb 15 2013 CROSSREFS Cf. A210278, A000680, A067630, A084939, A084940, A084941, A084942, A084943, A084944, A087127, A001147, A132101. Sequence in context: A123828 A260659 A351854 * A008563 A059487 A156932 Adjacent sequences: A210274 A210275 A210276 * A210278 A210279 A210280 KEYWORD nonn,easy AUTHOR Mohammad K. Azarian, Mar 20 2012 STATUS approved

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Last modified August 11 21:40 EDT 2024. Contains 375073 sequences. (Running on oeis4.)