A034825 Number of n-node rooted trees of height at most 8.

1, 1, 1, 2, 4, 9, 20, 48, 115, 286, 718, 1832, 4702, 12159, 31515, 81888, 212878, 553557, 1438741, 3737331, 9700188, 25156049, 65181067, 168746672, 436505846, 1128256918, 2914103577, 7521450053, 19400577711, 50010551503, 128841990772, 331754004302

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 A034824 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 6 do b[j]:= etr(shr(b[j-1])) od: a:= shr(b[6]): 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}, 8], 1] (* Geoffrey Critzer, Aug 01 2013 *)

Crossrefs

See A001383 for details.

Sequence in context: A318854 A255638 A215971 * A145546 A292553 A318802

Adjacent sequences: A034822 A034823 A034824 * A034826 A034827 A034828

Keyword

nonn

Author

N. J. A. Sloane.

Status

approved