A255520 Number of rooted identity trees with n nodes and 8-colored non-root nodes.

0, 1, 8, 92, 1304, 20198, 332520, 5703724, 100847976, 1824927697, 33634879304, 629201396744, 11915930584384, 228010216559592, 4401559021963488, 85616787777724400, 1676436841812675760, 33017479163392717192, 653643628799220208104, 12999812350464606307796

Offset: 0

Author

Alois P. Heinz, Feb 24 2015

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..750

Crossrefs

Column k=8 of A255517.

Programs

Maple

with(numtheory):
a:= proc(n) option remember; `if`(n<2, n, -add(a(n-j)*add(
      8*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 = 21.5622387024302370660187831154056800411286761376313324441779580180359..., c = 0.049440632575743414117260362085656158155861722... . - Vaclav Kotesovec, Feb 24 2015

From Ilya Gutkovskiy, Apr 14 2019: (Start)

G.f. A(x) satisfies: A(x) = x*exp(8*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)^(8*a(n)). (End)