%I A036361
%S A036361 0,1,1,6,70,1215,27951,799708,27337500,1086190605,49162945645,2496308717826,
%T A036361 140489907594114,8678436279296875,583701359488329915,42457773984656284920,
%U A036361 3320786296452525792376,277898747312921495246937,24775177557380767822265625
%N A036361 Number of labeled 2-trees with n nodes.
%D A036361 L. W. Beineke, R. E. Pippert, The number of labeled k-dimensional trees, 
               J. Combinatorial Theory 6 1969 200-205. Math. Rev. 38 #3182.
%D A036361 F. Harary and E. Palmer, Graphical Enumeration, (1973), p. 30.
%H A036361 T. D. Noe, <a href="b036361.txt">Table of n, a(n) for n=1..100</a>
%H A036361 <a href="Sindx_Tra.html#trees">Index entries for sequences related to 
               trees</a>
%F A036361 Number of labeled k-trees on n nodes is binomial(n, k) * (k(n-k)+1)^(n-k-2).
%p A036361 A036361 := n-> binomial(n,2)*(2*n-3)^(n-4);
%Y A036361 Cf. A000272 (labeled trees), A036361 (labeled 2-trees), A036362 (labeled 
               3-trees), A036506 (labeled 4-trees), A000055 (unlabeled trees), A054581 
               (unlabeled 2-trees).
%Y A036361 Sequence in context: A104900 A001448 A024489 this_sequence A050788 A027317 
               A099339
%Y A036361 Adjacent sequences: A036358 A036359 A036360 this_sequence A036362 A036363 
               A036364
%K A036361 nonn,easy,nice
%O A036361 1,4
%A A036361 N. J. A. Sloane (njas(AT)research.att.com).