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A006965 Number of directed trees with n nodes.
(Formerly M1677)
4
1, 2, 6, 25, 114, 591, 3298, 19532, 120687, 771373, 5061741, 33943662, 231751331, 1606587482, 11283944502, 80157645245, 575105238243, 4162624144308, 30365913761136, 223075674659696, 1649166676341180, 12262121068089094, 91649977839972636, 688288656744067230 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
REFERENCES
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
P. Leroux and B. Miloudi, Généralisations de la formule d'Otter, Ann. Sci. Math. Quebec, 1992, Vol. 16, No. 1, 53-80.
P. Leroux and B. Miloudi, Généralisations de la formule d'Otter, Ann. Sci. Math. Québec, Vol. 16, No. 1, pp. 53-80, 1992. (Annotated scanned copy)
MAPLE
with(combstruct):B:=x->add(3*count([S, {B = Set(S), S = Prod(B, B, B, Z)}, unlabeled], size=i)*x^i, i=1..50); seq(coeff(B(x)-B(x)^2/2+B(x^2)/2, x, n)/3, n=1..30); # with Algolib (Pab Ter)
# second Maple program:
b:= proc(n) option remember; `if`(n<2, 3*n, (add(add(b(d)
*d, d=numtheory[divisors](j))*b(n-j), j=1..n-1))/(n-1))
end:
a:= n-> `if`(n=0, 1, b(n)-(add(b(k) *b(n-k), k=0..n)-
`if`(irem(n, 2)=0, b(n/2), 0))/2)/3:
seq(a(n), n=1..30); # Alois P. Heinz, Jun 03 2020
MATHEMATICA
b[n_] := b[n] = If[n < 2, 3 n, (Sum[Sum[b[d] d, {d, Divisors[j]}] b[n - j], {j, 1, n - 1}])/(n - 1)];
a[n_] := If[n == 0, 1, b[n] - (Sum[b[k] b[n - k], {k, 0, n}] - If[Mod[n, 2] == 0, b[n/2], 0])/2]/3;
Array[a, 30] (* Jean-François Alcover, Nov 01 2020, after Alois P. Heinz *)
CROSSREFS
Equals (1/3) A038060(n).
Row sums of A335362.
Sequence in context: A229042 A269484 A014277 * A202705 A058801 A321720
KEYWORD
nonn
AUTHOR
STATUS
approved

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Last modified March 18 22:56 EDT 2024. Contains 370952 sequences. (Running on oeis4.)