A255521 Number of rooted identity trees with n nodes and 9-colored non-root nodes.

0, 1, 9, 117, 1866, 32553, 603414, 11654634, 232034283, 4728048201, 98125181461, 2066983603704, 44079196497075, 949772378078829, 20645820782745363, 452215682045713701, 9970925646977589555, 221133330528834114000, 4929622717525248345174, 110400838255998014848137

Offset: 0

Author

Alois P. Heinz, Feb 24 2015

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..700

Crossrefs

Column k=9 of A255517.

Programs

Maple

with(numtheory):
a:= proc(n) option remember; `if`(n<2, n, -add(a(n-j)*add(
      9*a(d)*d*(-1)^(j/d), d=divisors(j)), j=1..n-1)/(n-1))
    end:
seq(a(n), n=0..30);

Formula

a(n) ~ c * d^n / n^(3/2), where d = 24.2805556948066926165789325334976292249076194687965619357813839307368..., c = 0.04399000859622510673129847184312171422452194... . - Vaclav Kotesovec, Feb 24 2015

From Ilya Gutkovskiy, Apr 14 2019: (Start)

G.f. A(x) satisfies: A(x) = x*exp(9*Sum_{k>=1} (-1)^(k+1)*A(x^k)/k).

G.f.: A(x) = Sum_{n>=1} a(n)*x^n = x * Product_{n>=1} (1 + x^n)^(9*a(n)). (End)