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%I M2159 #27 Feb 16 2024 21:09:40
%S 0,1,2,36,1200,57000,3477600,257826240,22438563840,2238543216000,
%T 251584613280000,31431367287936000,4319334744012288000,
%U 647313578549730892800,105041172967733882880000,18345770194541665075200000,3430869798262479024291840000
%N Number of labeled plane 2-trees with n nodes.
%D F. Harary and E. Palmer, Graphical Enumeration, (1973), p. 30, Problem 1.14.
%D E. M. Palmer and R. C. Read, on the number of plane 2-trees, J. Lond. Math. Soc., 6 (1973), 583-592.
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H G. C. Greubel, <a href="/A003092/b003092.txt">Table of n, a(n) for n = 1..300</a>
%H Allan Bickle, <a href="https://digitalcommons.georgiasouthern.edu/cgi/viewcontent.cgi?article=1409&context=tag">A Survey of Maximal k-degenerate Graphs and k-Trees</a>, Theory and Applications of Graphs 0 1 (2024) Article 5.
%H E. M. Palmer and R. C. Read, <a href="/A003093/a003093.pdf">On the number of plane 2-trees</a>, J. Lond. Math. Soc., 6 (1973), 583-592. [Annotated and corrected scanned copy]
%H <a href="/index/Tra#trees">Index entries for sequences related to trees</a>
%F a(n) = n*(n-1)^2*(5*n-10)!/(4*n-6)!.
%p [0, seq(n*(n-1)^2*(5*n-10)!/(4*n-6)!, n=2..20) ];
%t Join[{0}, Table[n*(n-1)^2*(5*n-10)!/(4*n-6)!, {n,2,30}]] (* _G. C. Greubel_, Nov 02 2022 *)
%o (Magma) [0] cat [n*(n-1)^2*Factorial(5*n-10)/Factorial(4*n-6): n in [2..30]]; // _G. C. Greubel_, Nov 02 2022
%o (SageMath) [0]+[n*(n-1)^2*factorial(5*n-10)/factorial(4*n-6) for n in range(2,30)] # _G. C. Greubel_, Nov 02 2022
%K nonn
%O 1,3
%A _N. J. A. Sloane_
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