In this paper we consider the recurrent equation
$\Lambda_{p+1}=\frac{1}{p}\sum_{q=1}^pf\bigg(\frac{q}{p+1}\bigg)\Lambda _{q}\Lambda_{p+1-q}$
for
p≥1 with
f∈
C0,1] and Λ
1=
y>0 given. We give conditions on
f that guarantee the existence of
y (0) such that the sequence Λ
p with Λ
1=
y (0) tends to a finite positive limit as
p→∞.