%I #20 Dec 29 2014 18:24:06
%S 1,1,1,2,4,9,20,48,114,278,676,1653,4027,9816,23843,57833,139908,
%T 337856,814127,1958524,4703322,11278027,27003707,64571463,154207616,
%U 367841733,876450881,2086098057,4960230005,11782852600,27963874395,66307010599
%N Number of n-node rooted trees of height at most 6.
%H N. J. A. Sloane, <a href="/A034823/b034823.txt">Table of n, a(n) for n=0..200</a>
%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%H <a href="/index/Ro#rooted">Index entries for sequences related to rooted trees</a>
%F Take Euler transform of A001385 and shift right. (Christian G. Bower).
%p For Maple program see link in A000235.
%p 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
%t 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 *)
%Y See A001383 for details.
%K nonn
%O 0,4
%A _N. J. A. Sloane_.