Hello Pierre Charland,

>(n^4 - 2n^3 + 3n^2 - 2n + 8)/8 - (n^3 - 5n^2 + 6n)/2
> = (n^4 -6n^3 + 23n^2 -26n +8)/8
>
>

Oops! You are right of course; I seem to have had a little sign error in the final polynomial.

>Good work.

Thanks!

>
>------------------------------------------------------
>PS: After all this, (that is after I got your answer),
>I searched "7,18,41,85" on Google
>and found it in the Encyclopedia of Integer Sequences
>(It is not in the printed version I have)
>
>http://www.research.att.com/~njas/sequences/A055503
>where the following reference is given:
>L. Comtet, Advanced Combinatorics, Reidel, 1974, Problem 1,
>p. 72; and Problem 8, p. 74.

I've never used this encyclopedia, although I've heard others here speak of it. It looks like a useful tool, especially since Google can search it online.

This wraps up the question that started this thread, then, so now I'll go looking around for other fun questions. Thanks for an interesting discussion.

--Stuart Anderson