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
Alois P. Heinz, Table of n, a(n) for n = 1..500
Loïc Foissy, Algebraic structures on typed decorated rooted trees, arXiv:1811.07572 [math.RA], 2018.
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 439
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
KEYWORD
nonn,eigen
AUTHOR
EXTENSIONS
Extended by Christian G. Bower, Apr 15 1998
STATUS
approved