OFFSET
0,3
COMMENTS
Previous name was: A simple grammar.
Number of rooted trees with 5-colored non-root nodes. - Christian G. Bower, Sep 07 2002
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..870
L. Foissy, Algebraic structures on typed decorated rooted trees, arXiv:1811.07572 [math.RA], 2018-2021.
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 745.
FORMULA
a(n) ~ c * d^n / n^(3/2), where d = 13.78565111008468519893032491082181549507446564..., c = 0.0809706405011433830276324977466118885837... . - Vaclav Kotesovec, Aug 26 2014
G.f. A(x) satisfies: A(x) = x*exp(5*Sum_{k>=1} A(x^k)/k). - Ilya Gutkovskiy, Mar 19 2018
MAPLE
spec := [S, {B=Set(S), S=Prod(Z, B, B, B, B, B)}, unlabeled]: seq(combstruct[count](spec, size=n), n=0..20);
with(numtheory):
a:= proc(n) option remember; `if`(n<2, n, (add(add(d*
a(d), d=divisors(j))*a(n-j)*5, j=1..n-1))/(n-1))
end:
seq(a(n), n=0..25); # Vaclav Kotesovec, Aug 26 2014 after Alois P. Heinz
MATHEMATICA
a[n_] := a[n] = If[n<2, n, Sum[Sum[d*a[d], {d, Divisors[j]}]*a[n-j]*5, {j, 1, n-1}]/(n-1)]; Table[a[n], {n, 0, 25}] (* Jean-François Alcover, Feb 24 2016, adapted from Maple *)
CROSSREFS
KEYWORD
easy,nonn,eigen
AUTHOR
INRIA Encyclopedia of Combinatorial Structures, Jan 25 2000
EXTENSIONS
New name from Vaclav Kotesovec, Aug 26 2014
STATUS
approved