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A034825 Number of n-node rooted trees of height at most 8. 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,4
LINKS
N. J. A. Sloane, Transforms
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
KEYWORD
nonn
AUTHOR
STATUS
approved

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Last modified March 28 07:33 EDT 2024. Contains 371235 sequences. (Running on oeis4.)