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A006965
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Number of directed trees with n nodes.
(Formerly M1677)
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4
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1, 2, 6, 25, 114, 591, 3298, 19532, 120687, 771373, 5061741, 33943662, 231751331, 1606587482, 11283944502, 80157645245, 575105238243, 4162624144308, 30365913761136, 223075674659696, 1649166676341180, 12262121068089094, 91649977839972636, 688288656744067230
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OFFSET
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1,2
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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MAPLE
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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:
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MATHEMATICA
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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;
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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