This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A001384 M1172 N0449 #41 Dec 19 2021 09:58:04
%S A001384 1,1,1,2,4,9,19,42,89,191,402,847,1763,3667,7564,15564,31851,64987,
%T A001384 132031,267471,539949,1087004,2181796,4367927,8721533,17372967,
%U A001384 34524291,68456755,135446896,267444085,527027186,1036591718,2035083599
%N A001384 Number of n-node trees of height at most 4.
%C A001384 a(n+1) is also the number of n-vertex graphs that do not contain a P_4, C_4, or K_5 as induced subgraph (K_5-free trivially perfect graphs, cf. A123467). - _Falk Hüffner_, Jan 10 2016
%D A001384 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A001384 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A001384 N. J. A. Sloane, <a href="/A001384/b001384.txt">Table of n, a(n) for n=0..200</a>
%H A001384 INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=63">Encyclopedia of Combinatorial Structures 63</a>
%H A001384 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 A001384 N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%H A001384 <a href="/index/Ro#rooted">Index entries for sequences related to rooted trees</a>
%H A001384 <a href="/index/Tra#trees">Index entries for sequences related to trees</a>
%F A001384 Take Euler transform of A001383 and shift right. (_Christian G. Bower_)
%p A001384 For Maple program see link in A000235.
%p A001384 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: A000041:= etr(n->1): b1:= etr(k-> A000041(k-1)): A001383:= n->`if`(n=0,1,b1(n-1)): b2:= etr(A001383): a:= n->`if`(n=0,1,b2(n-1)): seq(a(n), n=0..40); # _Alois P. Heinz_, Sep 08 2008
%t A001384 Prepend[Nest[CoefficientList[Series[Product[1/(1-x^i)^#[[i]],{i,1,Length[#]}],{x,0,40}],x]&,{1},4],1] (* _Geoffrey Critzer_, Aug 01 2013 *)
%Y A001384 See A001383 for details.
%K A001384 nonn
%O A001384 0,4
%A A001384 _N. J. A. Sloane_