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%I #20 Dec 19 2014 20:27:38
%S 1,1,1,2,4,9,20,48,115,286,719,1841,4755,12410,32558,85849,226980,
%T 601373,1594870,4232100,11230771,29798539,79034638,209526631,
%U 555172356,1470195001,3891131705,10292857772,27212082536,71905725130,189911518888
%N Number of n-node rooted trees of height at most 9.
%H N. J. A. Sloane, <a href="/A034826/b034826.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 A034825 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 7 do b[j]:= etr(shr(b[j-1])) od: a:= shr(b[7]): seq(a(n), n=0..40); # _Alois P. Heinz_, Sep 08 2008
%t etr[p_] := Module[{b}, b[n_] := b[n] = If[n == 0, 1, Sum[Sum[d*p[d], {d, Divisors[j]}]*b[n-j], {j, 1, n}]/n]; b]; shr[p_] = If[# == 0, 1, p[#-1]]&; b[0] = etr[1&]; For[j = 1, j <= 7, j++, b[j] = etr[shr[b[j-1]]]]; a = shr[b[7]]; Table[a[n], {n, 0, 31}] (* _Jean-François Alcover_, Mar 10 2014, after _Alois P. Heinz_ *)
%Y See A001383 for details.
%K nonn
%O 0,4
%A _N. J. A. Sloane_.
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