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

0,3

Links

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

Formula

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

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);

Crossrefs

Column k=7 of A255517.

Sequence in context: A027394 A346767 A209327 * A305966 A226805 A113343

Adjacent sequences: A255516 A255517 A255518 * A255520 A255521 A255522

Keyword

nonn

Author

Alois P. Heinz, Feb 24 2015

Status

approved