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

0,3

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.

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

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 *)

Crossrefs

Column k=9 of A242249.

Sequence in context: A144073 A261801 A065086 * A234573 A306033 A065707

Adjacent sequences: A246235 A246236 A246237 * A246239 A246240 A246241

Keyword

nonn

Author

Alois P. Heinz, Aug 19 2014

Status

approved