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 A034824 #21 Jul 08 2025 21:27:41
%S A034824 1,1,1,2,4,9,20,48,115,285,710,1789,4514,11431,28922,73182,184917,
%T A034824 466755,1176393,2961205,7443770,18689435,46869152,117412440,293832126,
%U A034824 734645046,1835147741,4580420719,11423511895,28469058647,70899220083,176449174539,438854372942
%N A034824 Number of n-node rooted trees of height at most 7.
%H A034824 N. J. A. Sloane, <a href="/A034824/b034824.txt">Table of n, a(n) for n=0..200</a>
%H A034824 N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%H A034824 <a href="/index/Ro#rooted">Index entries for sequences related to rooted trees</a>
%F A034824 Take Euler transform of A034823 and shift right. (_Christian G. Bower_).
%p A034824 For Maple program see link in A000235.
%p A034824 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 5 do b[j]:= etr(shr(b[j-1])) od: a:= shr(b[5]): seq(a(n), n=0..35); # _Alois P. Heinz_, Sep 08 2008
%t A034824 Prepend[Nest[CoefficientList[Series[Product[1/(1-x^i)^#[[i]], {i, 1, Length[#]}], {x, 0, 40}], x]&, {1}, 7], 1] (* _Geoffrey Critzer_, Aug 01 2013 *)
%Y A034824 See A001383 for details.
%K A034824 nonn
%O A034824 0,4
%A A034824 _N. J. A. Sloane_