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

0,3

Links

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

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)

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);

Crossrefs

Column k=9 of A255517.

Sequence in context: A059967 A346769 A304184 * A027396 A294190 A113344

Adjacent sequences: A255518 A255519 A255520 * A255522 A255523 A255524

Keyword

nonn

Author

Alois P. Heinz, Feb 24 2015

Status

approved