n!*Fibonacci(n)

[Karol]

    Dear Brendan,


     Do you have also another version where you have not cheated ?
     Thanks in advance ,    Karol



Brendan McKay wrote:

>* Karol <penson at lptl.jussieu.fr> [050327 08:35]:
>  
>
>>      I wonder if  a combinatorial ( or other ) interpretation of the 
>>sequences
>>           n!*Fibonacci(n),   n!*Pell(n)...   etc . is known.
>>
>>                                Karol A. Penson
>>    
>>
>
>Suppose you have a lot of bricks. Some have height 1 and are
>labelled with a single positive integer. The others have height 2
>and are labelled with an ordered pair of two positive integers.
>Then n!*Fibonacci(n) is the number of ways of stacking up some
>bricks of total height n such that the integers 1,2,...,n each
>appear exactly once.
>
>I hope you can all see that I cheated!!
>
>Brendan.
>  
>