n!*Fibonacci(n)

[Peter Cameron]

On Sat, Mar 26, 2005 at 11:34:36PM +0100, Karol wrote:
> 
> 
>        I wonder if  a combinatorial ( or other ) interpretation of the 
> sequences
>             n!*Fibonacci(n),   n!*Pell(n)...   etc . is known.
>  
>                                  Karol A. Penson

Often one can find such an interpretation in the theory of species.
If the objects of a species have no non-trivial automorphisms, then an
n-element object can be labelled in n! ways, so the number of labelled
objects is n! times the number of unlabelled objects. There are various
ways of manufacturing species with these properties; the simplest is
by taking a linear order as part of the structure.

Peter Cameron.