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

0,3

Links

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

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)

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);

Crossrefs

Column k=8 of A255517.

Sequence in context: A346768 A027395 A277307 * A305967 A113353 A081624

Adjacent sequences: A255517 A255518 A255519 * A255521 A255522 A255523

Keyword

nonn

Author

Alois P. Heinz, Feb 24 2015

Status

approved