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%I #37 Mar 02 2024 13:03:10
%S 0,1,1,6,70,1215,27951,799708,27337500,1086190605,49162945645,
%T 2496308717826,140489907594114,8678436279296875,583701359488329915,
%U 42457773984656284920,3320786296452525792376,277898747312921495246937,24775177557380767822265625
%N Number of labeled 2-trees with n nodes.
%D F. Harary and E. Palmer, Graphical Enumeration, (1973), p. 30.
%H T. D. Noe, <a href="/A036361/b036361.txt">Table of n, a(n) for n = 1..100</a>
%H L. W. Beineke and R. E. Pipert, <a href="http://dx.doi.org/10.1016/S0021-9800(69)80120-1">The number of labeled k-dimensional trees</a>, J. Comb. Theory 6 (2) (1969) 200-205. Math. Rev. 38 #3182.
%H Allan Bickle, <a href="https://doi.org/10.20429/tag.2024.000105">A Survey of Maximal k-degenerate Graphs and k-Trees</a>, Theory and Applications of Graphs 0 1 (2024) Article 5.
%H T. Fowler, I. Gessel, G. Labelle and P. Leroux, <a href="https://doi.org/10.1006/aama.2001.0771">The specification of 2-trees</a>, Adv. Appl. Math. 28 (2) (2002) 145-168, eq. (18).
%H <a href="/index/Tra#trees">Index entries for sequences related to trees</a>
%F Number of labeled k-trees on n nodes is binomial(n, k) * (k(n-k)+1)^(n-k-2).
%p A036361:=n->binomial(n, 2)*(2*n-3)^(n-4): seq(A036361(n), n=1..30);
%t Table[Binomial[n,2](2n-3)^(n-4),{n,20}] (* _Harvey P. Dale_, Nov 24 2011 *)
%o (Python)
%o def A036361(n): return int(n*(n - 1)*(2*n - 3)**(n - 4)//2) # _Chai Wah Wu_, Feb 03 2022
%Y Column 3 of A135021.
%Y Cf. A000272 (labeled trees), this sequence (labeled 2-trees), A036362 (labeled 3-trees), A036506 (labeled 4-trees), A000055 (unlabeled trees), A054581 (unlabeled 2-trees).
%K nonn,easy,nice
%O 1,4
%A _N. J. A. Sloane_
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