A001385 Number of n-node trees of height at most 5. (Formerly M1177 N0453)

1, 1, 1, 2, 4, 9, 20, 47, 108, 252, 582, 1345, 3086, 7072, 16121, 36667, 83099, 187885, 423610, 953033, 2139158, 4792126, 10714105, 23911794, 53273599, 118497834, 263164833, 583582570, 1292276355, 2857691087, 6311058671, 13919982308, 30664998056, 67473574130

Offset

0,4

Comments

a(n+1) is also the number of n-vertex graphs that do not contain a P_4, C_4, or K_6 as induced subgraph (K_6-free trivially perfect graphs, cf. A123467). - Falk Hüffner, Jan 10 2016

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

N. J. A. Sloane, Table of n, a(n) for n=0..200

J. Riordan, Enumeration of trees by height and diameter, IBM J. Res. Dev. 4 (1960), 473-478.

N. J. A. Sloane, Transforms

Index entries for sequences related to rooted trees

Index entries for sequences related to trees

Formula

Take Euler transform of A001384 and shift right. (Christian G. Bower)

Maple

For Maple program see link in A000235.
with(numtheory): etr:= proc(p) local b; b:=proc(n) option remember; local d, j; if n=0 then 1 else add(add(d*p(d), d=divisors(j)) *b(n-j), j=1..n)/n fi end end: shr:= proc(p) n->`if`(n=0, 1, p(n-1)) end: b[0]:= etr(n->1): for j from 1 to 3 do b[j]:= etr(shr(b[j-1])) od: a:= shr(b[3]): seq(a(n), n=0..35); # Alois P. Heinz, Sep 08 2008

Mathematica

Prepend[Nest[CoefficientList[Series[Product[1/(1-x^i)^#[[i]], {i, 1, Length[#]}], {x, 0, 40}], x]&, {1}, 5], 1] (* Geoffrey Critzer, Aug 01 2013 *)

Crossrefs

See A001383 for details.

Sequence in context: A104508 A368830 A036623 * A039808 A138164 A130802

Adjacent sequences: A001382 A001383 A001384 * A001386 A001387 A001388

Keyword

nonn

Author

N. J. A. Sloane

Status

approved