A000299 Number of n-node rooted trees of height 4.

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

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

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.
• J. Riordan, The enumeration of trees by height and diameter, IBM Journal 4 (1960), 473-478. (Annotated scanned copy)
• Index entries for sequences related to rooted trees
• Index entries for sequences related to trees

Crossrefs

Column h=4 of A034781.

Programs

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 *)

Formula

Cf. A001384-A001383. - Christian G. Bower