Part-products of 1-free integer compositions (Q665756)

Summary: If \(\vec \lambda \) is a composition of the positive integer \(n\), define \(\mathbf B(\vec \lambda )\) to be the product of the parts of \(\vec \lambda \). We present a modified version of Hitczenko's stopped sequence construction that leads to a proof of the asymptotic lognormality of \(\mathbf B\) for random 1-free compositions (compositions containing no parts of size 1).