A034823 Number of n-node rooted trees of height at most 6.

1, 1, 1, 2, 4, 9, 20, 48, 114, 278, 676, 1653, 4027, 9816, 23843, 57833, 139908, 337856, 814127, 1958524, 4703322, 11278027, 27003707, 64571463, 154207616, 367841733, 876450881, 2086098057, 4960230005, 11782852600, 27963874395, 66307010599

Offset

0,4

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

Formula

Take Euler transform of A001385 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 4 do b[j]:= etr(shr(b[j-1])) od: a:= shr(b[4]): seq(a(n), n=0..31); # Alois P. Heinz, Sep 08 2008

Mathematica

Prepend[Nest[CoefficientList[Series[Product[1/(1-x^i)^#[[i]], {i, 1, Length[#]}], {x, 0, 40}], x]&, {1}, 6], 1] (* Geoffrey Critzer, Aug 01 2013 *)

Crossrefs

See A001383 for details.

Sequence in context: A036624 A226907 A186952 * A036625 A003019 A036626

Adjacent sequences: A034820 A034821 A034822 * A034824 A034825 A034826

Keyword

nonn

Author

N. J. A. Sloane.

Status

approved