[duskwuff]

That's the number of unique combinations of clues for all 2^25 puzzles. There are 13 possible clues for each row/column (0 1 2 3 4 5 11 12 13 21 22 31 111), but not all 13^10 possible combinations can appear together - for instance, 5 5 5 5 5 / 0 0 0 0 0 is obviously impossible.

(I wrote a program to calculate this by generating all 2^25 puzzles and their clues, then sorting by the clues. I also verified the count of 25,309,575 clues with unique solutions.)

[ghusbands]

That's great, thanks. I've also independently verified the 25,309,575 using similar techniques.