A255519 Number of rooted identity trees with n nodes and 7-colored non-root nodes.

0, 1, 7, 70, 868, 11746, 169022, 2533895, 39156244, 619261762, 9974917309, 163078496420, 2699109217420, 45136794135853, 761492594770649, 12944937176754422, 221518183089901621, 3812823547509811611, 65966582592220602621, 1146568019260356348978

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=7 of A255517.

Programs

Maple

with(numtheory):
a:= proc(n) option remember; `if`(n<2, n, -add(a(n-j)*add(
      7*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 = 18.843901825822305757579605844910623225182677164912157727486865738745..., c = 0.056432508184666421552433382560980970822794... . - Vaclav Kotesovec, Feb 24 2015

From Ilya Gutkovskiy, Apr 13 2019: (Start)

G.f. A(x) satisfies: A(x) = x*exp(7*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)^(7*a(n)). (End)