A034823 Number of n-node rooted trees of height at most 6.

1, 1, 1, 2, 4, 9, 20, 48, 114, 278, 676, 1653, 4027, 9816, 23843, 57833, 139908, 337856, 814127, 1958524, 4703322, 11278027, 27003707, 64571463, 154207616, 367841733, 876450881, 2086098057, 4960230005, 11782852600, 27963874395, 66307010599

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Links

• N. J. A. Sloane, Table of n, a(n) for n=0..200
• N. J. A. Sloane, Transforms
• Index entries for sequences related to rooted trees

Crossrefs

See A001383 for details.

Programs

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 4 do b[j]:= etr(shr(b[j-1])) od: a:= shr(b[4]): seq(a(n), n=0..31); # 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},6],1] (* Geoffrey Critzer, Aug 01 2013 *)

Formula

Take Euler transform of A001385 and shift right. (Christian G. Bower).