This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A036362 #21 Mar 02 2024 13:10:24
%S A036362 0,0,1,1,10,200,5915,229376,10946964,618435840,40283203125,
%T A036362 2968444272640,243926836708126,22100985366992896,2187905889450121295,
%U A036362 234881024000000000000,27172548942138551952680,3369317755618569294053376,445726953911853022186520169
%N A036362 Number of labeled 3-trees with n nodes.
%D A036362 F. Harary and E. Palmer, Graphical Enumeration, (1973), p. 30, Problem 1.13(b) with k=3.
%H A036362 T. D. Noe, <a href="/A036362/b036362.txt">Table of n, a(n) for n=1..100</a>
%H A036362 <a href="/index/Tra#trees">Index entries for sequences related to trees</a>
%F A036362 a(n) = binomial(n, 3)*(3*n-8)^(n-5).
%F A036362 Number of labeled k-trees on n nodes is binomial(n, k) * (k(n-k)+1)^(n-k-2).
%p A036362 [ seq(binomial(n,3)*(3*n-8)^(n-5), n=1..20) ];
%t A036362 Table[Binomial[n,3](3n-8)^(n-5),{n,20}] (* _Harvey P. Dale_, Dec 31 2023 *)
%o A036362 (Python)
%o A036362 def A036362(n): return int(n*(n - 2)*(n - 1)*(3*n - 8)**(n - 5)//6) # _Chai Wah Wu_, Feb 03 2022
%Y A036362 Column 4 of A135021.
%Y A036362 Cf. A000272 (labeled trees), A036361 (labeled 2-trees), this sequence (labeled 3-trees), A036506 (labeled 4-trees), A000055 (unlabeled trees), A054581 (unlabeled 2-trees).
%K A036362 nonn,easy
%O A036362 1,5
%A A036362 _N. J. A. Sloane_