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%I #17 Aug 01 2013 19:44:47
%S 1,1,1,2,4,9,20,48,115,286,718,1832,4702,12159,31515,81888,212878,
%T 553557,1438741,3737331,9700188,25156049,65181067,168746672,436505846,
%U 1128256918,2914103577,7521450053,19400577711,50010551503,128841990772,331754004302
%N Number of n-node rooted trees of height at most 8.
%H N. J. A. Sloane, <a href="/A034825/b034825.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 A034824 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 6 do b[j]:= etr(shr(b[j-1])) od: a:= shr(b[6]): 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}, 8], 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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