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

0,3

Links

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

Formula

a(n) ~ c * d^n / n^(3/2), where d = 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)

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);

Crossrefs

Column k=10 of A255517.

Sequence in context: A180905 A062744 A059968 * A113354 A027397 A305969

Adjacent sequences: A255519 A255520 A255521 * A255523 A255524 A255525

Keyword

nonn

Author

Alois P. Heinz, Feb 24 2015

Status

approved