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A006964 Number of directed rooted trees with n nodes.
(Formerly M2994)
11
1, 3, 15, 82, 495, 3144, 20875, 142773, 1000131, 7136812, 51702231, 379234623, 2810874950, 21020047557, 158398829121, 1201617201230, 9169060501023, 70329406653879, 541949364313821, 4193569906262874, 32571403998781956, 253842927519362734, 1984442128649393178 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Also rooted trees with n nodes and 3-colored non-root nodes. - Christian G. Bower, Apr 15 1998
REFERENCES
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
Loïc Foissy, Algebraic structures on typed decorated rooted trees, arXiv:1811.07572 [math.RA], 2018.
P. Leroux and B. Miloudi, Généralisations de la formule d'Otter, Ann. Sci. Mathh
. Québec, Vol. 16, No. 1 (1992) pp. 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)
R. J. Mathar, Topologically Distinct Sets of Non-intersecting Circles in the Plane, arXiv:1603.00077 [math.CO], 2016.
FORMULA
a(n+1) has g.f.: Product_{n>=1} (1 - x^3*a(n))^-1.
a(n) ~ c * d^n / n^(3/2), where d = 8.356026879295995368276069578708912..., c = 0.13645899548680457355557420025756... . - Vaclav Kotesovec, Aug 20 2014
G.f. A(x) satisfies: A(x) = x*exp(3*Sum_{k>=1} A(x^k)/k). - Ilya Gutkovskiy, Mar 19 2018
MAPLE
with(numtheory): a:= proc(n) option remember; `if`(n<2, n, (add(add(d*a(d), d=divisors(j)) *a(n-j)*3, j=1..n-1))/(n-1)) end: seq(a(n), n=1..30); # Alois P. Heinz, Sep 06 2008
MATHEMATICA
a[n_] := a[n] = If[n<2, n, (Sum[Sum[d*a[d], {d, Divisors[j]}]*a[n-j]*3, {j, 1, n-1}])/(n-1)]; Table[a[n], {n, 1, 30}] (* Jean-François Alcover, Mar 30 2015, after Alois P. Heinz *)
CROSSREFS
Cf. A038059.
Column k=3 of A242249.
Sequence in context: A059271 A345885 A014276 * A203507 A192662 A213096
KEYWORD
nonn,eigen
AUTHOR
EXTENSIONS
Extended by Christian G. Bower, Apr 15 1998
STATUS
approved

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Last modified March 1 14:57 EST 2024. Contains 370433 sequences. (Running on oeis4.)