AIME II #6 2008

[stupidityismygam]

The sequence [unparseable or potentially dangerous latex formula] is defined by

[unparseable or potentially dangerous latex formula] and [unparseable or potentially dangerous latex formula] for [unparseable or potentially dangerous latex formula]

The sequence [unparseable or potentially dangerous latex formula] is defined by

[unparseable or potentially dangerous latex formula] and [unparseable or potentially dangerous latex formula] for [unparseable or potentially dangerous latex formula]

Find [unparseable or potentially dangerous latex formula]

[Michael T]

First few terms of a:
1,1,2,6,24,120 (*gasp* factorials! <--lol)
[unparseable or potentially dangerous latex formula] (Since n starts at 0, anyway)

First few terms of b:
1,3,12,60,360
Hmm...Multiply everything by two.
2,6,24,120,720 *gasp* more factorials.
[unparseable or potentially dangerous latex formula]

So [unparseable or potentially dangerous latex formula]
And [unparseable or potentially dangerous latex formula]
[unparseable or potentially dangerous latex formula]

I missed this because I failed to note the first term was at n=0 : (

EDIT: okay, wow, someone please remind me how to some basically LaTeX stuff (e.g. subscripts/division bars.)

[collegebookworm]