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 A036361 Number of labeled 2-trees with n nodes. 7
 0, 1, 1, 6, 70, 1215, 27951, 799708, 27337500, 1086190605, 49162945645, 2496308717826, 140489907594114, 8678436279296875, 583701359488329915, 42457773984656284920, 3320786296452525792376, 277898747312921495246937, 24775177557380767822265625 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 REFERENCES L. W. Beineke, R. E. Pippert, The number of labeled k-dimensional trees, J. Combinatorial Theory 6 1969 200-205. Math. Rev. 38 #3182. F. Harary and E. Palmer, Graphical Enumeration, (1973), p. 30. LINKS T. D. Noe, Table of n, a(n) for n=1..100 T. Fowler, I. Gessel, G. Labelle, P. Leroux, The specification of 2-trees, Adv. Appl. Math. 28 (2) (2002) 145-168, eq. (18). FORMULA Number of labeled k-trees on n nodes is binomial(n, k) * (k(n-k)+1)^(n-k-2). MAPLE A036361:=n->binomial(n, 2)*(2*n-3)^(n-4): seq(A036361(n), n=1..30); MATHEMATICA Table[Binomial[n, 2](2n-3)^(n-4), {n, 20}] (* Harvey P. Dale, Nov 24 2011 *) CROSSREFS Cf. A000272 (labeled trees), A036361 (labeled 2-trees), A036362 (labeled 3-trees), A036506 (labeled 4-trees), A000055 (unlabeled trees), A054581 (unlabeled 2-trees). Sequence in context: A186667 A001448 A024489 * A182563 A211036 A284215 Adjacent sequences:  A036358 A036359 A036360 * A036362 A036363 A036364 KEYWORD nonn,easy,nice AUTHOR STATUS approved

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Last modified May 27 13:33 EDT 2018. Contains 304690 sequences. (Running on oeis4.)