So, given $A,B,C,D,E,\ldots$ etc (up to $n$ letters) and $1,2,3,4,5,\ldots$ (up to $n$ numbers) where $n$ is the same for both (same number of letters as numbers)
How many unique sequences of letters and numbers can be formed such that for the $i^\text{th}$ number in the sequence, there are at least $i$ preceding letters.
So for example
- $A1B2C3$
- $AB12C3$
- $ABC123$
But not
- $1ABC23$
- $AB123C$