Sequences whose terms are equal to the number of functions with specified properties are considered. Properties are based on the notion of derangements in a more general sense. Several sequences which generalize the standard notion of derangements are thus obtained. These sequences generate a number of integer sequences from the well-known Sloane's encyclopedia.
Integer sequences and matrices over finite fields
The On-Line Encyclopedia of Integer Sequences
Two New Integer Sequences Related to Crossroads and Catalan Numbers
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