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A255521
Number of rooted identity trees with n nodes and 9-colored non-root nodes.
2
0, 1, 9, 117, 1866, 32553, 603414, 11654634, 232034283, 4728048201, 98125181461, 2066983603704, 44079196497075, 949772378078829, 20645820782745363, 452215682045713701, 9970925646977589555, 221133330528834114000, 4929622717525248345174, 110400838255998014848137
OFFSET
0,3
LINKS
FORMULA
a(n) ~ c * d^n / n^(3/2), where d = 24.2805556948066926165789325334976292249076194687965619357813839307368..., c = 0.04399000859622510673129847184312171422452194... . - Vaclav Kotesovec, Feb 24 2015
From Ilya Gutkovskiy, Apr 14 2019: (Start)
G.f. A(x) satisfies: A(x) = x*exp(9*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)^(9*a(n)). (End)
MAPLE
with(numtheory):
a:= proc(n) option remember; `if`(n<2, n, -add(a(n-j)*add(
9*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=9 of A255517.
Sequence in context: A059967 A346769 A304184 * A027396 A294190 A113344
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Feb 24 2015
STATUS
approved