A255522 Number of rooted identity trees with n nodes and 10-colored non-root nodes.

0, 1, 10, 145, 2570, 49860, 1027602, 22068705, 488541820, 11068982545, 255437694060, 5983042467096, 141873247900650, 3399140192819340, 82160878859739650, 2001070766525744725, 49061025740711233080, 1209873601374566796515, 29990547373994063764080

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=10 of A255517.

Programs

Maple

with(numtheory):
a:= proc(n) option remember; `if`(n<2, n, -add(a(n-j)*add(
      10*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 = 26.998860838916733933849490675388336975888308433826638445291076817..., c = 0.0396216952587990270999387393053224285... . - Vaclav Kotesovec, Feb 24 2015

From Ilya Gutkovskiy, Apr 14 2019: (Start)

G.f. A(x) satisfies: A(x) = x*exp(10*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)^(10*a(n)). (End)