This is the unique minimum degree interpolated polynomial:
$$
-\frac{23}{15}n^5+\frac{175}{6}n^4-\frac{572}{3}n^3+\frac{3329}{6}n^2-\frac{3559}{5}n+324
$$
whose values at $1,2,\ldots,6$ are $4,12,24,48,240,720$.

This can be found using GAP via:

InterpolatedPolynomial(Integers,[1,2,3,4,5,6],[4,12,24,48,240,720]);


While this is unlikely the answer you are looking for (since it has a negative leading coefficient and is of the maximum degree possible; moreover, your sequence appears to grow around $O(n!)$, whereas this polynomial grows as $O(n^5)$), you're probably not going to get a better answer without explaining what the sequence actually is.

Can we represent this sequence as a function of n?
We filter and analyse seats for events.  Apparently writing a domain query language for the floor people isn't an option.  I'm using C# 4.0 &amp; .NET 4.0, and have relatively free reign to use whatever open-source tools are available.  &lt;/background-info&gt;

If a request comes in for "FLOOR B", the sales people want it to show up if they've entered "FLOOR A-FLOOR F" in a filter.  The only problem I have is that there's absolutely no structure to the parsed parameters.  I get the string already concatenated (it actually uses a tilde instead of dash).  Examples I've seen so far with matches after each:


101WC-199WC  (needs to match 150WC)
AAA-ZZZ   (needs to match AAA, BBB, ABC but not BB)
LOGE15-LOGE20  (needs to match LOGE15 but not LOGE150)


At first I wanted to try just stripping off the numeric part of the lower and upper, and then incrementing through that.  The problem I have is that only some entries have numbers, sometimes the numbers AND letters increment, sometimes its all letters that increment.  Since I can't impose any kind of grammar to use (I really wanted [..] expansion syntax), I'm stuck using these entries.

Are there any suggestions for how to approach this parsing problem?
