It's a great solution that doesn't assume the three numbers(25,50 and 100)

It's just the opposite.

For future readers Collections.sort(..,Collections.reverseOrder());

It took me a few min to realise that its a good one haha

Dont mean to burden with this simple operation but I'm left a bit confused on the !(weight % 2) can someone shed some light on this...

inefficient way of implementing simple method using heavy libraries.

Finally a solution which goes the generic way ! I love it ! The value-specific logic proposed in most solutions horrifies me to no end ...

A bit over the top for the task, but solution uses OOP and a decent lookup algorithm which could handle other bills than the ones given in the instructions without codechange.
+Clever for this. (Reverted +BestPractce since it is somewhat contrary to the Effective Java Recommendations, like extending a Hashmap instead of wrapping one).

The condition for n === 1 is actually unnecessary, since if n = 1, triangular(1 - 1) + 1 = triangular(0) + 1 = 0 + 1 = 1.

Indeed, it does call triangular(0), which returns 0, which is added to the recursive summation, causing no change to the value:
triangular(4) =
triangular(3) + 4 =
triangular(2) + 3 + 4 =
triangular(1) + 2 + 3 + 4 =
triangular(0) + 1 + 2 + 3 + 4 =
0 + 1 + 2 + 3 + 4 =
10