A034826 Number of n-node rooted trees of height at most 9.

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

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Links

• N. J. A. Sloane, Table of n, a(n) for n=0..200
• N. J. A. Sloane, Transforms
• Index entries for sequences related to rooted trees

Crossrefs

See A001383 for details.

Programs

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 *)

Formula

Take Euler transform of A034825 and shift right. (Christian G. Bower).