Calculating odds of rolling a given total with a specified number of dice

[Thomas Klemm]

Just tested it with HP-48GX.
You start with a 64-dimensional vector:

[0, 0, … , 0 , 0, 1, 1, 1, 1, 1, 1]

Run the discrete Fourier transform:

FFT

Transmogrify the result to a list of 64 complex numbers:

OBJ→
OBJ→
DROP
→LIST

{ (6,0) (5.5701807… }

Apply the 9th power (point-wise):

9 y^x

{ (10077696,0) (-8… }

Transmogrify back to a vector:

OBJ→
{ }
+
→ARRY

Compute the inverse Fourier transform:

IFFT

[ (.00000034,0) (.… ]

Drawback is that you have now an array of complex numbers that are nearly real.
Thus transmogrify back to a list and run:

ABS
0 RND

And finally you have the list of coefficients:

{ 0 0 0 0 0 0 0 0 0
0 1 9 45 165 495
1287 2994 6354
12465 22825 39303

Of course the list is a little longer than just that.

Cheers
Thomas