%I A036362
%S A036362 0,0,1,1,10,200,5915,229376,10946964,618435840,40283203125,2968444272640,
%T A036362 243926836708126,22100985366992896,2187905889450121295,234881024000000000000,
%U A036362 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="b036362.txt">Table of n, a(n) for n=1..100</a>
%H A036362 <a href="Sindx_Tra.html#trees">Index entries for sequences related to 
               trees</a>
%F A036362 C(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) ];
%Y A036362 Cf. A000272, A036361.
%Y A036362 Cf. A000272 (labeled trees), A036361 (labeled 2-trees), A036362 (labeled 
               3-trees), A036506 (labeled 4-trees), A000055 (unlabeled trees), A054581 
               (unlabeled 2-trees).
%Y A036362 Sequence in context: A079436 A126431 A156275 this_sequence A051262 A041183 
               A041180
%Y A036362 Adjacent sequences: A036359 A036360 A036361 this_sequence A036363 A036364 
               A036365
%K A036362 nonn,easy
%O A036362 1,5
%A A036362 N. J. A. Sloane (njas(AT)research.att.com).