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A255519
Number of rooted identity trees with n nodes and 7-colored non-root nodes.
2
0, 1, 7, 70, 868, 11746, 169022, 2533895, 39156244, 619261762, 9974917309, 163078496420, 2699109217420, 45136794135853, 761492594770649, 12944937176754422, 221518183089901621, 3812823547509811611, 65966582592220602621, 1146568019260356348978
OFFSET
0,3
LINKS
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
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Feb 24 2015
STATUS
approved