A246238 Number of rooted trees with n nodes and 9-colored non-root nodes.

0, 1, 9, 126, 2028, 35919, 674964, 13225632, 267188229, 5525568297, 116400215521, 2488984609644, 53883301460607, 1178671076752803, 26011822261355487, 578441979200964897, 12948907700868521142, 291569232606979152321, 6599274332502483541080

Offset: 0

Author

Alois P. Heinz, Aug 19 2014

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..500
• Loïc Foissy, Algebraic structures on typed decorated rooted trees, arXiv:1811.07572 [math.RA], 2018.

Crossrefs

Column k=9 of A242249.

Programs

Maple

with(numtheory):
a:= proc(n) option remember; `if`(n<2, n, (add(add(d*
      a(d), d=divisors(j))*a(n-j)*9, j=1..n-1))/(n-1))
    end:
seq(a(n), n=0..25);

Mathematica

a[n_] := a[n] = If[n<2, n, Sum[Sum[d*a[d], {d, Divisors[j]}]*a[n-j]*9, {j, 1, n-1}]/(n-1)];
Table[a[n], {n, 0, 25}] (* Jean-François Alcover, Feb 23 2019, from Maple *)

Formula

a(n) ~ c * d^n / n^(3/2), where d = 24.654188324989308481297681284616076174..., c = 0.044677658292795889027452779147731609565... . - Vaclav Kotesovec, Aug 26 2014

G.f. A(x) satisfies: A(x) = x*exp(9*Sum_{k>=1} A(x^k)/k). - Ilya Gutkovskiy, Mar 20 2018