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%I M1177 N0453 #34 Dec 19 2021 09:58:17
%S 1,1,1,2,4,9,20,47,108,252,582,1345,3086,7072,16121,36667,83099,
%T 187885,423610,953033,2139158,4792126,10714105,23911794,53273599,
%U 118497834,263164833,583582570,1292276355,2857691087,6311058671,13919982308,30664998056,67473574130
%N Number of n-node trees of height at most 5.
%C 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
%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H N. J. A. Sloane, <a href="/A001385/b001385.txt">Table of n, a(n) for n=0..200</a>
%H J. Riordan, <a href="http://dx.doi.org/10.1147/rd.45.0473">Enumeration of trees by height and diameter</a>, IBM J. Res. Dev. 4 (1960), 473-478.
%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>
%H <a href="/index/Tra#trees">Index entries for sequences related to trees</a>
%F Take Euler transform of A001384 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 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
%t 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 *)
%Y See A001383 for details.
%K nonn
%O 0,4
%A _N. J. A. Sloane_
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