A000299 Number of n-node rooted trees of height 4. (Formerly M3461 N1408)

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

1,6

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.

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

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

N. J. A. Sloane

Status

approved