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 A034826 Number of n-node rooted trees of height at most 9. 2
 1, 1, 1, 2, 4, 9, 20, 48, 115, 286, 719, 1841, 4755, 12410, 32558, 85849, 226980, 601373, 1594870, 4232100, 11230771, 29798539, 79034638, 209526631, 555172356, 1470195001, 3891131705, 10292857772, 27212082536, 71905725130, 189911518888 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 LINKS N. J. A. Sloane, Table of n, a(n) for n=0..200 N. J. A. Sloane, Transforms FORMULA Take Euler transform of A034825 and shift right. (Christian G. Bower). MAPLE For Maple program see link in A000235. 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 MATHEMATICA 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 *) CROSSREFS See A001383 for details. Sequence in context: A318855 A255639 A216062 * A145547 A292554 A318803 Adjacent sequences:  A034823 A034824 A034825 * A034827 A034828 A034829 KEYWORD nonn AUTHOR STATUS approved

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Last modified June 2 13:42 EDT 2020. Contains 334780 sequences. (Running on oeis4.)