Dice probabilities

[John Keith]

(05-01-2024 04:41 AM)Thomas Klemm Wrote:  

(04-30-2024 10:00 PM)John Keith Wrote:  No real need for Wolfram Alpha, though. On the HP 50 (…)

True. But I can't post a link to your HP-50, can I?

(04-30-2024 10:00 PM)John Keith Wrote:  (…) the Haskell program at A027907 is very fast and easy to implement using DOLIST.

Please don't leave us hanging here. Just post your program.

Simpler than I thought using ADD instead of DOLIST.

Given n on stack, returns row n of A027907 (2n + 1 coefficients).

Code:


/<< { 1 1 1 } 2 ROT
  START 0 OVER + 0 +
    { 0 0 } ROT DUP2 SWAP + UNROT +
    ADD ADD
  NEXT
\>>

For HP48G, use ROT ROT instead of UNROT, also some coefficients will not be exact if n > 27 because they are > 10^12.

And now a dumb question: Why can trinomial coefficients be used for any number of dice and faces per die? Are there cases where one may need tetranomial or higher order coefficients?