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Generating functions for the number of permutations with limited displacement. (English) Zbl 1186.05012

Summary: Let \(V(d,n)\) be the number of permutations \(p\) of \(\{1,2,\dots,n\}\) that satisfy \(|p_i-i|\leq d\) for all \(i\). Generating functions for \(V(d,n)\), for fixed \(d\), are given.

MSC:

05A15 Exact enumeration problems, generating functions
94B60 Other types of codes
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Online Encyclopedia of Integer Sequences:

a(n) = (2^n + C(2*n,n))/2.