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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, Table of n, a(n) for n=0..200 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 Adjacent sequences:  A034822 A034823 A034824 * A034826 A034827 A034828 KEYWORD nonn AUTHOR STATUS approved

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Last modified June 7 05:20 EDT 2020. Contains 334837 sequences. (Running on oeis4.)