A034824 Number of n-node rooted trees of height at most 7.

1, 1, 1, 2, 4, 9, 20, 48, 115, 285, 710, 1789, 4514, 11431, 28922, 73182, 184917, 466755, 1176393, 2961205, 7443770, 18689435, 46869152, 117412440, 293832126, 734645046, 1835147741, 4580420719, 11423511895, 28469058647, 70899220083, 176449174539, 438854372942

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 A034823 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 5 do b[j]:= etr(shr(b[j-1])) od: a:= shr(b[5]): seq(a(n), n=0..35); # 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}, 7], 1] (* Geoffrey Critzer, Aug 01 2013 *)

Crossrefs

See A001383 for details.

Sequence in context: A318853 A255637 A215796 * A145545 A182378 A318801

Adjacent sequences: A034821 A034822 A034823 * A034825 A034826 A034827

Keyword

nonn

Author

N. J. A. Sloane.

Status

approved