login
A255518
Number of rooted identity trees with n nodes and 6-colored non-root nodes.
2
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
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
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Feb 24 2015
STATUS
approved