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%I #24 Mar 22 2022 09:52:35
%S 1,6,56,720,11880,240240,5765760,160392960,5079110400,180503769600,
%T 7117005772800,308403583488000,14572069319808000,745747076954880000,
%U 41098950018846720000,2427001153744527360000,152901072685905223680000
%N Number of labeled plane 2-trees on n triangles.
%H Andrew Howroyd, <a href="/A093197/b093197.txt">Table of n, a(n) for n = 2..200</a>
%H G. Labelle, C. Lamathe and P. Leroux, <a href="https://arxiv.org/abs/math/0202052">A classification of plane and planar 2-trees</a>, arXiv:math/0202052 [math.CO], 2002.
%F a(n) = n! * (2/3 * C(n) - 1/6 * C(n+1)), where C(n) = A000108(n).
%F a(n) = RisingFactorial(5 + n, n) assuming offset 0. - _Peter Luschny_, Mar 22 2022
%t a[n_]:=n! * (2/3 * CatalanNumber[n] - 1/6 * CatalanNumber[n+1]); Array[a,50,2] (* _Stefano Spezia_, Sep 01 2018 *)
%o (PARI) a(n)=if(n < 2, 0, n!*(4*binomial(2*n,n)/(n+1)-binomial(2*n+2,n+1)/(n+2))/6) \\ _Andrew Howroyd_, Aug 31 2018
%K nonn
%O 2,2
%A _Ralf Stephan_, Apr 22 2004