A joint central limit theorem for the
and asymptotic divisibility of Catalan-like sequences
We prove a central limit theorem for the
joint distribution of sq(Ajn),
1 <= j <= d, where sq denotes
the sum-of-digits function in base q and the
Aj's are positive integers
relatively prime to q. We do this in fact within the framework
of quasi-additive functions.
As application, we show that most elements of
"Catalan-like" sequences - by which we mean integer sequences
defined by products/quotients of factorials - are divisible by
any given positive integer.
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