Author:
Benoumhani Moussa,Heim Bernhard,Neuhauser Markus
Abstract
AbstractWe study arithmetic and asymptotic properties of polynomials provided by $$Q_n(x):= x \sum _{k=1}^n k \, Q_{n-k}(x)$$
Q
n
(
x
)
:
=
x
∑
k
=
1
n
k
Q
n
-
k
(
x
)
with initial value $$Q_0(x)=1$$
Q
0
(
x
)
=
1
. The coefficients satisfy a central limit theorem and a local limit theorem involving Fibonacci numbers. We apply the methods of Berry and Esseen, Harper, Bender, and Canfield.
Publisher
Springer Science and Business Media LLC
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