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 A000299 Number of n-node rooted trees of height 4. (Formerly M3461 N1408) 2
 0, 0, 0, 0, 1, 4, 13, 36, 93, 225, 528, 1198, 2666, 5815, 12517, 26587, 55933, 116564, 241151, 495417, 1011950, 2055892, 4157514, 8371318, 16792066, 33564256, 66875221, 132849983, 263192599, 520087551, 1025295487, 2016745784, 3958608430, 7754810743 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,6 REFERENCES N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence). N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS Alois P. Heinz, Table of n, a(n) for n = 1..1000 (first 200 terms from N. J. A. Sloane) F. Harary & R. W. Robinson, The number of achiral trees, Jnl. Reine Angewandte Mathematik 278 (1975), 322-335. (Annotated scanned copy) J. Riordan, Enumeration of trees by height and diameter, IBM J. Res. Dev. 4 (1960), 473-478. FORMULA Cf. A001384-A001383. - Christian G. Bower MAPLE For Maple program see link in A000235. MATHEMATICA f[n_] := Nest[CoefficientList[Series[Product[1/(1 - x^i)^#[[i]], {i, 1, Length[#]}], {x, 0, 40}], x] &, {1}, n]; f[4]-f[3] (* Geoffrey Critzer, Aug 01 2013 *) CROSSREFS Column h=4 of A034781. Sequence in context: A235996 A036636 A036643 * A102301 A206603 A271176 Adjacent sequences:  A000296 A000297 A000298 * A000300 A000301 A000302 KEYWORD nonn AUTHOR STATUS approved

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