I came up with a solution for this in 84+(CE) Basic. Note that if you have multiple words they must be entered without spaces.

**Code:** ```
Input "WORD=?",Str1
```

Prompt N

Delvar L₃length(Str1→dim(L₃

For(I,1,Ans

inString(Str1,sub(Str1,I,1

1+L₃(Ans→L₃(Ans

End

{N!→L₁

For(I,1,dim(L₃

Ans→L₂

For(J,1,L₃(I

augment({0},L₂/J→L₂

Ans+augment(L₁,{0→L₁

End

End

Ans(N+1

Perhaps out of habit I wrote this in an almost obfuscatedly optimized way, but let's break down what's going on here.

First, I delete L₃ and set its size to the length of the word (this ensures it is initialized to all zeros). This list will be used to accumulate the frequency of each letter.

**Code:** `Delvar L₃length(Str1→dim(L₃`

Next, loop I from 1 to the length of the string (which is in Ans from the previous line).

**Code:** `For(I,1,Ans`

Now, find the index of the first occurence of the I-th letter in the word. This effectively maps each distinct letter to a unique integer.

**Code:** `inString(Str1,sub(Str1,I,1`

Now that we have the mapped index, increment the corresponding element of L₃, and loop to the next letter.

**Code:** ```
1+L₃(Ans→L₃(Ans
```

End

At this point, each non-zero element of L₃ holds a letter frequency. For example, in the case of STATEMEET, it would be {1,3,1,0,3,1,0,0,0}.

Now, we'll use lists to represent polynomials for the generating function approach. Index 1 of a list will be the constant term, index 2 will be the coefficient of x, index 3 will be the coefficient of x˛, and so on.

We start with the polynomial (which we'll call P) with N! as a constant term in L₁.

**Code:** `{N!→L₁`

Now, we loop over each letter frequency to multiply its corresponding generating polynomial.

**Code:** `For(I,1,dim(L₃`

Here, we initialize L₂ to P (which is in Ans) times x^0 / 0! (that is, the constant term of 1 present in each generating polynomial).

**Code:** `Ans→L₂`

Now, we loop J from 1 to the current letter frequency to add in P times x^J / J!. (This loop is implicitly skipped for any 0-frequency element of L₃.)

**Code:** `For(J,1,L₃(I`

At the moment, L₂ is P times x^(J-1) / (J-1)!. To transform this into P times x^J / J!, we prepend a 0 (effectively multiplying by x) and divide by J.

**Code:** `augment({0},L₂/J→L₂`

Here, we add the resulting polynomial to L₁ (to which we append a 0 so the number of list elements match), and loop to the next exponent.

**Code:** ```
Ans+augment(L₁,{0→L₁
```

End

Now L₁ (and Ans) is the new value of P, so loop to the next letter frequency.

**Code:** `End`

Finally, we extract the coefficient of x^N from the resulting polynomial.

**Code:** `Ans(N+1`

Let me know if you have any questions!