A255518 Number of rooted identity trees with n nodes and 6-colored non-root nodes.

0, 1, 6, 51, 542, 6273, 77262, 991264, 13109394, 177428496, 2445799878, 34218909015, 484668543660, 6935979521095, 100136840127534, 1456726481340477, 21332234689262126, 314211310198197978, 4652073871301311128, 69194159284034697860, 1033441834436615884266

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..800

Formula

a(n) ~ c * d^n / n^(3/2), where d = 16.1255293604485586705050971466317639696978222052989685416919877643317..., c = 0.065726585606326795496161701400246926800764944... . - Vaclav Kotesovec, Feb 24 2015

From Ilya Gutkovskiy, Apr 13 2019: (Start)

G.f. A(x) satisfies: A(x) = x*exp(6*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)^(6*a(n)). (End)

Maple

with(numtheory):
a:= proc(n) option remember; `if`(n<2, n, -add(a(n-j)*add(
      6*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=6 of A255517.

Sequence in context: A027393 A346766 A305965 * A208250 A253097 A345259

Adjacent sequences: A255515 A255516 A255517 * A255519 A255520 A255521

Keyword

nonn

Author

Alois P. Heinz, Feb 24 2015

Status

approved